(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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