4x*x+2x-6=2(x*x-x)

Solution for 4x*x+2x-6=2(x*x-x) equation:

Simplifying
4x * x + 2x + -6 = 2(x * x + -1x)

Multiply x * x
4x2 + 2x + -6 = 2(x * x + -1x)

Reorder the terms:
-6 + 2x + 4x2 = 2(x * x + -1x)

Multiply x * x
-6 + 2x + 4x2 = 2(x2 + -1x)

Reorder the terms:
-6 + 2x + 4x2 = 2(-1x + x2)
-6 + 2x + 4x2 = (-1x * 2 + x2 * 2)
-6 + 2x + 4x2 = (-2x + 2x2)

Solving
-6 + 2x + 4x2 = -2x + 2x2

Solving for variable 'x'.

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

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

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

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

Combine like terms: -2x + 2x = 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 + x2) = 0

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

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