(5x-8)(4x-5)=0

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Solution for (5x-8)(4x-5)=0 equation:


Simplifying
(5x + -8)(4x + -5) = 0

Reorder the terms:
(-8 + 5x)(4x + -5) = 0

Reorder the terms:
(-8 + 5x)(-5 + 4x) = 0

Multiply (-8 + 5x) * (-5 + 4x)
(-8(-5 + 4x) + 5x * (-5 + 4x)) = 0
((-5 * -8 + 4x * -8) + 5x * (-5 + 4x)) = 0
((40 + -32x) + 5x * (-5 + 4x)) = 0
(40 + -32x + (-5 * 5x + 4x * 5x)) = 0
(40 + -32x + (-25x + 20x2)) = 0

Combine like terms: -32x + -25x = -57x
(40 + -57x + 20x2) = 0

Solving
40 + -57x + 20x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5 + -4x)(8 + -5x) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(8 + -5x)' equal to zero and attempt to solve: Simplifying 8 + -5x = 0 Solving 8 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -5x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -5x = 0 + -8 -5x = 0 + -8 Combine like terms: 0 + -8 = -8 -5x = -8 Divide each side by '-5'. x = 1.6 Simplifying x = 1.6

Solution

x = {1.25, 1.6}

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