-4x=2x^2-6

Solution for -4x=2x^2-6 equation:

Simplifying
-4x = 2x2 + -6

Reorder the terms:
-4x = -6 + 2x2

Solving
-4x = -6 + 2x2

Solving for variable 'x'.

Reorder the terms:
6 + -4x + -2x2 = -6 + 2x2 + 6 + -2x2

Reorder the terms:
6 + -4x + -2x2 = -6 + 6 + 2x2 + -2x2

Combine like terms: -6 + 6 = 0
6 + -4x + -2x2 = 0 + 2x2 + -2x2
6 + -4x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
6 + -4x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -2x + -1x2) = 0

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

Ignore the factor 2.
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 '(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
Solution
x = {1, -3}