x^2-x-40=-2x+2

Solution for x^2-x-40=-2x+2 equation:

Simplifying
x2 + -1x + -40 = -2x + 2

Reorder the terms:
-40 + -1x + x2 = -2x + 2

Reorder the terms:
-40 + -1x + x2 = 2 + -2x

Solving
-40 + -1x + x2 = 2 + -2x

Solving for variable 'x'.

Reorder the terms:
-40 + -2 + -1x + 2x + x2 = 2 + -2x + -2 + 2x

Combine like terms: -40 + -2 = -42
-42 + -1x + 2x + x2 = 2 + -2x + -2 + 2x

Combine like terms: -1x + 2x = 1x
-42 + 1x + x2 = 2 + -2x + -2 + 2x

Reorder the terms:
-42 + 1x + x2 = 2 + -2 + -2x + 2x

Combine like terms: 2 + -2 = 0
-42 + 1x + x2 = 0 + -2x + 2x
-42 + 1x + x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
-42 + 1x + x2 = 0

Factor a trinomial.
(-7 + -1x)(6 + -1x) = 0

Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-7, 6}