4x^2-2x=6(2x-1)

Solution for 4x^2-2x=6(2x-1) equation:

Simplifying
4x2 + -2x = 6(2x + -1)

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

Reorder the terms:
-2x + 4x2 = 6(-1 + 2x)
-2x + 4x2 = (-1 * 6 + 2x * 6)
-2x + 4x2 = (-6 + 12x)

Solving
-2x + 4x2 = -6 + 12x

Solving for variable 'x'.

Reorder the terms:
6 + -2x + -12x + 4x2 = -6 + 12x + 6 + -12x

Combine like terms: -2x + -12x = -14x
6 + -14x + 4x2 = -6 + 12x + 6 + -12x

Reorder the terms:
6 + -14x + 4x2 = -6 + 6 + 12x + -12x

Combine like terms: -6 + 6 = 0
6 + -14x + 4x2 = 0 + 12x + -12x
6 + -14x + 4x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
6 + -14x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -7x + 2x2) = 0

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

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
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 = {0.5, 3}