(x-2)(x+3)=x+10

Solution for (x-2)(x+3)=x+10 equation:

Simplifying
(x + -2)(x + 3) = x + 10

Reorder the terms:
(-2 + x)(x + 3) = x + 10

Reorder the terms:
(-2 + x)(3 + x) = x + 10

Multiply (-2 + x) * (3 + x)
(-2(3 + x) + x(3 + x)) = x + 10
((3 * -2 + x * -2) + x(3 + x)) = x + 10
((-6 + -2x) + x(3 + x)) = x + 10
(-6 + -2x + (3 * x + x * x)) = x + 10
(-6 + -2x + (3x + x2)) = x + 10

Combine like terms: -2x + 3x = 1x
(-6 + 1x + x2) = x + 10

Reorder the terms:
-6 + 1x + x2 = 10 + x

Solving
-6 + 1x + x2 = 10 + x

Solving for variable 'x'.

Reorder the terms:
-6 + -10 + 1x + -1x + x2 = 10 + x + -10 + -1x

Combine like terms: -6 + -10 = -16
-16 + 1x + -1x + x2 = 10 + x + -10 + -1x

Combine like terms: 1x + -1x = 0
-16 + 0 + x2 = 10 + x + -10 + -1x
-16 + x2 = 10 + x + -10 + -1x

Reorder the terms:
-16 + x2 = 10 + -10 + x + -1x

Combine like terms: 10 + -10 = 0
-16 + x2 = 0 + x + -1x
-16 + x2 = x + -1x

Combine like terms: x + -1x = 0
-16 + x2 = 0

Factor a difference between two squares.
(4 + x)(-4 + x) = 0

Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Subproblem 2
Set the factor '(-4 + x)' equal to zero and attempt to solve:

Simplifying
-4 + x = 0

Solving
-4 + x = 0

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

Add '4' to each side of the equation.
-4 + 4 + x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + x = 0 + 4
x = 0 + 4

Combine like terms: 0 + 4 = 4
x = 4

Simplifying
x = 4
Solution
x = {-4, 4}