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

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


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

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

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

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

Combine like terms: -5x + -8x = -13x
(2 + -13x + 20x2) = 0

Solving
2 + -13x + 20x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -4x)(2 + -5x) = 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 '(2 + -5x)' equal to zero and attempt to solve: Simplifying 2 + -5x = 0 Solving 2 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -5x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5x = 0 + -2 -5x = 0 + -2 Combine like terms: 0 + -2 = -2 -5x = -2 Divide each side by '-5'. x = 0.4 Simplifying x = 0.4

Solution

x = {0.25, 0.4}

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