(2x-2)(5x-4)=0

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Solution for (2x-2)(5x-4)=0 equation: 


Simplifying
(2x + -2)(5x + -4) = 0

Reorder the terms:
(-2 + 2x)(5x + -4) = 0

Reorder the terms:
(-2 + 2x)(-4 + 5x) = 0

Multiply (-2 + 2x) * (-4 + 5x)
(-2(-4 + 5x) + 2x * (-4 + 5x)) = 0
((-4 * -2 + 5x * -2) + 2x * (-4 + 5x)) = 0
((8 + -10x) + 2x * (-4 + 5x)) = 0
(8 + -10x + (-4 * 2x + 5x * 2x)) = 0
(8 + -10x + (-8x + 10x2)) = 0

Combine like terms: -10x + -8x = -18x
(8 + -18x + 10x2) = 0

Solving
8 + -18x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + -9x + 5x2) = 0

Factor a trinomial.
2((4 + -5x)(1 + -1x)) = 0

Ignore the factor 2.

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 '(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 = {0.8, 1}

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