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

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


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

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

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

Multiply (-4 + 5x) * (-5 + 4x)
(-4(-5 + 4x) + 5x * (-5 + 4x)) = 0
((-5 * -4 + 4x * -4) + 5x * (-5 + 4x)) = 0
((20 + -16x) + 5x * (-5 + 4x)) = 0
(20 + -16x + (-5 * 5x + 4x * 5x)) = 0
(20 + -16x + (-25x + 20x2)) = 0

Combine like terms: -16x + -25x = -41x
(20 + -41x + 20x2) = 0

Solving
20 + -41x + 20x2 = 0

Solving for variable 'x'.

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

Subproblem 1

Set the factor '(4 + -5x)' equal to zero and attempt to solve: Simplifying 4 + -5x = 0 Solving 4 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -5x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5x = 0 + -4 -5x = 0 + -4 Combine like terms: 0 + -4 = -4 -5x = -4 Divide each side by '-5'. x = 0.8 Simplifying x = 0.8

Subproblem 2

Set the factor '(5 + -4x)' equal to zero and attempt to solve: Simplifying 5 + -4x = 0 Solving 5 + -4x = 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 + -4x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4x = 0 + -5 -4x = 0 + -5 Combine like terms: 0 + -5 = -5 -4x = -5 Divide each side by '-4'. x = 1.25 Simplifying x = 1.25

Solution

x = {0.8, 1.25}

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