10x-2x^2=12

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

Simplifying
10x + -2x2 = 12

Solving
10x + -2x2 = 12

Solving for variable 'x'.

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

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

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + 5x + -1x2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + x)' equal to zero and attempt to solve:

Simplifying
-3 + x = 0

Solving
-3 + x = 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 + x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + x = 0 + 3
x = 0 + 3

Combine like terms: 0 + 3 = 3
x = 3

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