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

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

Simplifying
3x2 + -7x = 2x2 + -12

Reorder the terms:
-7x + 3x2 = 2x2 + -12

Reorder the terms:
-7x + 3x2 = -12 + 2x2

Solving
-7x + 3x2 = -12 + 2x2

Solving for variable 'x'.

Reorder the terms:
12 + -7x + 3x2 + -2x2 = -12 + 2x2 + 12 + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
12 + -7x + 1x2 = -12 + 2x2 + 12 + -2x2

Reorder the terms:
12 + -7x + 1x2 = -12 + 12 + 2x2 + -2x2

Combine like terms: -12 + 12 = 0
12 + -7x + 1x2 = 0 + 2x2 + -2x2
12 + -7x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
12 + -7x + 1x2 = 0

Factor a trinomial.
(3 + -1x)(4 + -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 '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {3, 4}