(4x-1)(2x-5)=0

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Solution for (4x-1)(2x-5)=0 equation:


Simplifying
(4x + -1)(2x + -5) = 0

Reorder the terms:
(-1 + 4x)(2x + -5) = 0

Reorder the terms:
(-1 + 4x)(-5 + 2x) = 0

Multiply (-1 + 4x) * (-5 + 2x)
(-1(-5 + 2x) + 4x * (-5 + 2x)) = 0
((-5 * -1 + 2x * -1) + 4x * (-5 + 2x)) = 0
((5 + -2x) + 4x * (-5 + 2x)) = 0
(5 + -2x + (-5 * 4x + 2x * 4x)) = 0
(5 + -2x + (-20x + 8x2)) = 0

Combine like terms: -2x + -20x = -22x
(5 + -22x + 8x2) = 0

Solving
5 + -22x + 8x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -4x)(5 + -2x) = 0

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 '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5

Solution

x = {0.25, 2.5}

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