(2x-1)(4x-3)=0

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Solution for (2x-1)(4x-3)=0 equation:


Simplifying
(2x + -1)(4x + -3) = 0

Reorder the terms:
(-1 + 2x)(4x + -3) = 0

Reorder the terms:
(-1 + 2x)(-3 + 4x) = 0

Multiply (-1 + 2x) * (-3 + 4x)
(-1(-3 + 4x) + 2x * (-3 + 4x)) = 0
((-3 * -1 + 4x * -1) + 2x * (-3 + 4x)) = 0
((3 + -4x) + 2x * (-3 + 4x)) = 0
(3 + -4x + (-3 * 2x + 4x * 2x)) = 0
(3 + -4x + (-6x + 8x2)) = 0

Combine like terms: -4x + -6x = -10x
(3 + -10x + 8x2) = 0

Solving
3 + -10x + 8x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -2x)(3 + -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 '(3 + -4x)' equal to zero and attempt to solve: Simplifying 3 + -4x = 0 Solving 3 + -4x = 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 + -4x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4x = 0 + -3 -4x = 0 + -3 Combine like terms: 0 + -3 = -3 -4x = -3 Divide each side by '-4'. x = 0.75 Simplifying x = 0.75

Solution

x = {0.5, 0.75}

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