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

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


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

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

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

Combine like terms: 5x + 20x = 25x
(-25 + 25x + -4x2) = 0

Solving
-25 + 25x + -4x2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve:

Simplifying
-5 + x = 0

Solving
-5 + x = 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 + x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + x = 0 + 5
x = 0 + 5

Combine like terms: 0 + 5 = 5
x = 5

Simplifying
x = 5

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 = {5, 1.25}

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