(2x-1)(5x-1)=4(2x-1)

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Solution for (2x-1)(5x-1)=4(2x-1) equation: 


Simplifying
(2x + -1)(5x + -1) = 4(2x + -1)

Reorder the terms:
(-1 + 2x)(5x + -1) = 4(2x + -1)

Reorder the terms:
(-1 + 2x)(-1 + 5x) = 4(2x + -1)

Multiply (-1 + 2x) * (-1 + 5x)
(-1(-1 + 5x) + 2x * (-1 + 5x)) = 4(2x + -1)
((-1 * -1 + 5x * -1) + 2x * (-1 + 5x)) = 4(2x + -1)
((1 + -5x) + 2x * (-1 + 5x)) = 4(2x + -1)
(1 + -5x + (-1 * 2x + 5x * 2x)) = 4(2x + -1)
(1 + -5x + (-2x + 10x2)) = 4(2x + -1)

Combine like terms: -5x + -2x = -7x
(1 + -7x + 10x2) = 4(2x + -1)

Reorder the terms:
1 + -7x + 10x2 = 4(-1 + 2x)
1 + -7x + 10x2 = (-1 * 4 + 2x * 4)
1 + -7x + 10x2 = (-4 + 8x)

Solving
1 + -7x + 10x2 = -4 + 8x

Solving for variable 'x'.

Reorder the terms:
1 + 4 + -7x + -8x + 10x2 = -4 + 8x + 4 + -8x

Combine like terms: 1 + 4 = 5
5 + -7x + -8x + 10x2 = -4 + 8x + 4 + -8x

Combine like terms: -7x + -8x = -15x
5 + -15x + 10x2 = -4 + 8x + 4 + -8x

Reorder the terms:
5 + -15x + 10x2 = -4 + 4 + 8x + -8x

Combine like terms: -4 + 4 = 0
5 + -15x + 10x2 = 0 + 8x + -8x
5 + -15x + 10x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
5 + -15x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(1 + -3x + 2x2) = 0

Factor a trinomial.
5((1 + -2x)(1 + -1x)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5

Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

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

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

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {0.5, 1}

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