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

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


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

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

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

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

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

Combine like terms: -16x + -25x = -41x
x(20 + -41x + 20x2) = 0
(20 * x + -41x * x + 20x2 * x) = 0
(20x + -41x2 + 20x3) = 0

Solving
20x + -41x2 + 20x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(20 + -41x + 20x2) = 0

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


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0

Subproblem 2
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 3
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, 0.8, 1.25}

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