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

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


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

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

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

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

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

Solving
-1 + 2x + 8x2 = 0

Solving for variable 'x'.

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

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 '(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 = {-0.5, 0.25}

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