(x-2)(x+10)=13

Solution for (x-2)(x+10)=13 equation:

Simplifying
(x + -2)(x + 10) = 13

Reorder the terms:
(-2 + x)(x + 10) = 13

Reorder the terms:
(-2 + x)(10 + x) = 13

Multiply (-2 + x) * (10 + x)
(-2(10 + x) + x(10 + x)) = 13
((10 * -2 + x * -2) + x(10 + x)) = 13
((-20 + -2x) + x(10 + x)) = 13
(-20 + -2x + (10 * x + x * x)) = 13
(-20 + -2x + (10x + x2)) = 13

Combine like terms: -2x + 10x = 8x
(-20 + 8x + x2) = 13

Solving
-20 + 8x + x2 = 13

Solving for variable 'x'.

Reorder the terms:
-20 + -13 + 8x + x2 = 13 + -13

Combine like terms: -20 + -13 = -33
-33 + 8x + x2 = 13 + -13

Combine like terms: 13 + -13 = 0
-33 + 8x + x2 = 0

Factor a trinomial.
(-11 + -1x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-11 + -1x)' equal to zero and attempt to solve:

Simplifying
-11 + -1x = 0

Solving
-11 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '11' to each side of the equation.
-11 + 11 + -1x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1x = 0 + 11
-1x = 0 + 11

Combine like terms: 0 + 11 = 11
-1x = 11

Divide each side by '-1'.
x = -11

Simplifying
x = -11
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-11, 3}