4x(2x-1)+2(2x-1)(2x-1)=0

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Solution for 4x(2x-1)+2(2x-1)(2x-1)=0 equation:


Simplifying
4x(2x + -1) + 2(2x + -1)(2x + -1) = 0

Reorder the terms:
4x(-1 + 2x) + 2(2x + -1)(2x + -1) = 0
(-1 * 4x + 2x * 4x) + 2(2x + -1)(2x + -1) = 0
(-4x + 8x2) + 2(2x + -1)(2x + -1) = 0

Reorder the terms:
-4x + 8x2 + 2(-1 + 2x)(2x + -1) = 0

Reorder the terms:
-4x + 8x2 + 2(-1 + 2x)(-1 + 2x) = 0

Multiply (-1 + 2x) * (-1 + 2x)
-4x + 8x2 + 2(-1(-1 + 2x) + 2x * (-1 + 2x)) = 0
-4x + 8x2 + 2((-1 * -1 + 2x * -1) + 2x * (-1 + 2x)) = 0
-4x + 8x2 + 2((1 + -2x) + 2x * (-1 + 2x)) = 0
-4x + 8x2 + 2(1 + -2x + (-1 * 2x + 2x * 2x)) = 0
-4x + 8x2 + 2(1 + -2x + (-2x + 4x2)) = 0

Combine like terms: -2x + -2x = -4x
-4x + 8x2 + 2(1 + -4x + 4x2) = 0
-4x + 8x2 + (1 * 2 + -4x * 2 + 4x2 * 2) = 0
-4x + 8x2 + (2 + -8x + 8x2) = 0

Reorder the terms:
2 + -4x + -8x + 8x2 + 8x2 = 0

Combine like terms: -4x + -8x = -12x
2 + -12x + 8x2 + 8x2 = 0

Combine like terms: 8x2 + 8x2 = 16x2
2 + -12x + 16x2 = 0

Solving
2 + -12x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -6x + 8x2) = 0

Factor a trinomial.
2((1 + -4x)(1 + -2x)) = 0

Ignore the factor 2.

Subproblem 1

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

Subproblem 2

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

Solution

x = {0.25, 0.5}

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