x^2-7x+12=x-3

Solution for x^2-7x+12=x-3 equation:

Simplifying
x2 + -7x + 12 = x + -3

Reorder the terms:
12 + -7x + x2 = x + -3

Reorder the terms:
12 + -7x + x2 = -3 + x

Solving
12 + -7x + x2 = -3 + x

Solving for variable 'x'.

Reorder the terms:
12 + 3 + -7x + -1x + x2 = -3 + x + 3 + -1x

Combine like terms: 12 + 3 = 15
15 + -7x + -1x + x2 = -3 + x + 3 + -1x

Combine like terms: -7x + -1x = -8x
15 + -8x + x2 = -3 + x + 3 + -1x

Reorder the terms:
15 + -8x + x2 = -3 + 3 + x + -1x

Combine like terms: -3 + 3 = 0
15 + -8x + x2 = 0 + x + -1x
15 + -8x + x2 = x + -1x

Combine like terms: x + -1x = 0
15 + -8x + x2 = 0

Factor a trinomial.
(3 + -1x)(5 + -1x) = 0

Subproblem 1
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
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 = {3, 5}