(1.)  x2 - 5x - 6 = 0              here is the problem

(x - 6)(x + 1) = 0           factor

x - 6 = 0    x + 1 = 0   set each factor equal to 0

+ 6  +6      -1  -1   add this to each side
____________   __________
x = 6    ,    x = -1   add

result:  x = 6,  x = -1

(2.)   x2 - 5x + 6 = 0             here is the problem

(x - 2)(x - 3) = 0               factor

x - 2 = 0   x - 3 = 0    set each factor equal to 0

+ 2  +2    +   3  +3   add this to each side
_________ ______________
x = 2  ,    x = 3      add

result:  x = 2  ,  x = 3

(3.)  x2 - 3x - 10 = 0         here is the problem

(x - 5)(x + 2) = 0           factors

x - 5 = 0    x + 2 = 0    set each factor equal to 0

+ 5  +5      - 2  -2   add this to each side
_________ ___________
x  = 5  ,    x =  -2    add

result:  x = 5  ,  x = -2

(4.)  n2 + n = 0               here is the problem

n(n + 1) = 0                 factor

n = 0    n + 1 = 0   set each factor equal to 0

-1  -1  subtract 1 from each side
________ _____________

n = 0  ,     n = -1    subtract

result:  n = 1 ,  x = -1

(5.)   y2 + 7y = 0           here is the problem

y(y + 7) = 0               factor

y = 0    y + 7 = 0       set each factor equal to 0

-7  -7       subtract 7 from each side
__________ ___________
y = 0   ,    y = -7        subtract

result:  y = 0 , y = -7

(6.)  c2 - 49 = 0               here is the problem

(c - 7)(c + 7) = 0              factor

c - 7 = 0    c + 7 = 0    set each factor equal to 0

+  7 + 7    - 7   -7    add this to each side
___________ _____________
c = 7   ,    c = -7     add

(7.)  3x2 - 2 = x2 + 6           here is the problem

+    2      + 2        add 2 to each side
_____________________
3x2   =  x2 + 8          add

-x2    -x2           subtract x2 from each side
__________________
2x2  =       8         subtract

____       _____
2           2         divide each side by 2

x2 = 4                   divide and cancel

-4  -4          subtract 4 from each side
_______________
x2 - 4 = 0           subtract

(x - 2)(x + 2) = 0           factor

x - 2 = 0    x + 2 = 0      set each factor equal to 0

+ 2 +2     -  2  -2   add this to each side
_______________ ______________
x = 2     ,   x = -2  add

result:  x = 2  ,  x = -2

(8.)  23p - 6 = -4p2                here is the problem

+4p2       + 4p2          add 4p2 to each side
_____________________
4p2 + 23p - 6 = 0                  add

(4p - 1)(p + 6) = 0                factor

4p - 1 = 0   p + 6 = 0    set each factor equal to 0

+  1 +1     - 6  -6    add this to each side
____________ _____________
4p  =   1  ,    p = -6        add
___     __
4       4               divide each side by 4

p = 1/4    ,  p = -6

result:  p = 1/4   ,    p = -6

(9.)   p3 - 13p2 + 36p = 0        here is the problem

p(p2 - 13p + 36) = 0         factor

p(p - 4)(p - 9) = 0             factor

p = 0   p - 4 = 0   p - 9 = 0   set each factor equal to 0

+4  +4   +  9  +9   add this to each side
____   __________  _________
p = 0 ,   p = 4  ,   p = 9       add

result:  p = 0 , p = 4, p = 9

(10.)   y3 - 16y2 = 0               here is the problem

y2(y - 16) = 0               factor

y = 0   y - 16 = 0    set each factor equal to 0

+ 16 +16     add 16 to each side
_________ _______________
y = 0  ,    y = 16       add

result:  y = 0 ,   y = 16