x^2-5x-7=x-12

Solution for x^2-5x-7=x-12 equation:

Simplifying
x2 + -5x + -7 = x + -12

Reorder the terms:
-7 + -5x + x2 = x + -12

Reorder the terms:
-7 + -5x + x2 = -12 + x

Solving
-7 + -5x + x2 = -12 + x

Solving for variable 'x'.

Reorder the terms:
-7 + 12 + -5x + -1x + x2 = -12 + x + 12 + -1x

Combine like terms: -7 + 12 = 5
5 + -5x + -1x + x2 = -12 + x + 12 + -1x

Combine like terms: -5x + -1x = -6x
5 + -6x + x2 = -12 + x + 12 + -1x

Reorder the terms:
5 + -6x + x2 = -12 + 12 + x + -1x

Combine like terms: -12 + 12 = 0
5 + -6x + x2 = 0 + x + -1x
5 + -6x + x2 = x + -1x

Combine like terms: x + -1x = 0
5 + -6x + x2 = 0

Factor a trinomial.
(1 + -1x)(5 + -1x) = 0

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {1, 5}