4-2(4x-3)x=2

Solution for 4-2(4x-3)x=2 equation:

Simplifying
4 + -2(4x + -3) * x = 2

Reorder the terms:
4 + -2(-3 + 4x) * x = 2

Reorder the terms for easier multiplication:
4 + -2x(-3 + 4x) = 2
4 + (-3 * -2x + 4x * -2x) = 2
4 + (6x + -8x2) = 2

Solving
4 + 6x + -8x2 = 2

Solving for variable 'x'.

Reorder the terms:
4 + -2 + 6x + -8x2 = 2 + -2

Combine like terms: 4 + -2 = 2
2 + 6x + -8x2 = 2 + -2

Combine like terms: 2 + -2 = 0
2 + 6x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 3x + -4x2) = 0

Factor a trinomial.
2((1 + -1x)(1 + 4x)) = 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 '(1 + 4x)' equal to zero and attempt to solve:

Simplifying
1 + 4x = 0

Solving
1 + 4x = 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 + 4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4x = 0 + -1
4x = 0 + -1

Combine like terms: 0 + -1 = -1
4x = -1

Divide each side by '4'.
x = -0.25

Simplifying
x = -0.25
Solution
x = {1, -0.25}