(5-4x)*(x-1)=4*(x-1)*x

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Solution for (5-4x)*(x-1)=4*(x-1)*x equation: 


Simplifying
(5 + -4x)(x + -1) = 4(x + -1) * x

Reorder the terms:
(5 + -4x)(-1 + x) = 4(x + -1) * x

Multiply (5 + -4x) * (-1 + x)
(5(-1 + x) + -4x * (-1 + x)) = 4(x + -1) * x
((-1 * 5 + x * 5) + -4x * (-1 + x)) = 4(x + -1) * x
((-5 + 5x) + -4x * (-1 + x)) = 4(x + -1) * x
(-5 + 5x + (-1 * -4x + x * -4x)) = 4(x + -1) * x
(-5 + 5x + (4x + -4x2)) = 4(x + -1) * x

Combine like terms: 5x + 4x = 9x
(-5 + 9x + -4x2) = 4(x + -1) * x

Reorder the terms:
-5 + 9x + -4x2 = 4(-1 + x) * x

Reorder the terms for easier multiplication:
-5 + 9x + -4x2 = 4x(-1 + x)
-5 + 9x + -4x2 = (-1 * 4x + x * 4x)
-5 + 9x + -4x2 = (-4x + 4x2)

Solving
-5 + 9x + -4x2 = -4x + 4x2

Solving for variable 'x'.

Reorder the terms:
-5 + 9x + 4x + -4x2 + -4x2 = -4x + 4x2 + 4x + -4x2

Combine like terms: 9x + 4x = 13x
-5 + 13x + -4x2 + -4x2 = -4x + 4x2 + 4x + -4x2

Combine like terms: -4x2 + -4x2 = -8x2
-5 + 13x + -8x2 = -4x + 4x2 + 4x + -4x2

Reorder the terms:
-5 + 13x + -8x2 = -4x + 4x + 4x2 + -4x2

Combine like terms: -4x + 4x = 0
-5 + 13x + -8x2 = 0 + 4x2 + -4x2
-5 + 13x + -8x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-5 + 13x + -8x2 = 0

Factor a trinomial.
(-1 + x)(5 + -8x) = 0


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

Simplifying
-1 + x = 0

Solving
-1 + x = 0

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

Add '1' to each side of the equation.
-1 + 1 + x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + x = 0 + 1
x = 0 + 1

Combine like terms: 0 + 1 = 1
x = 1

Simplifying
x = 1

Subproblem 2
Set the factor '(5 + -8x)' equal to zero and attempt to solve:

Simplifying
5 + -8x = 0

Solving
5 + -8x = 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 + -8x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -8x = 0 + -5
-8x = 0 + -5

Combine like terms: 0 + -5 = -5
-8x = -5

Divide each side by '-8'.
x = 0.625

Simplifying
x = 0.625
Solution
x = {1, 0.625}

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