2x^2=10x-12

Solution for 2x^2=10x-12 equation:

Simplifying
2x2 = 10x + -12

Reorder the terms:
2x2 = -12 + 10x

Solving
2x2 = -12 + 10x

Solving for variable 'x'.

Reorder the terms:
12 + -10x + 2x2 = -12 + 10x + 12 + -10x

Reorder the terms:
12 + -10x + 2x2 = -12 + 12 + 10x + -10x

Combine like terms: -12 + 12 = 0
12 + -10x + 2x2 = 0 + 10x + -10x
12 + -10x + 2x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
12 + -10x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + -5x + x2) = 0

Factor a trinomial.
2((2 + -1x)(3 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Subproblem 2
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
Solution
x = {2, 3}