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

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


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

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

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

Multiply (-5 + 5x) * (-5 + 2x)
(-5(-5 + 2x) + 5x * (-5 + 2x)) = 0
((-5 * -5 + 2x * -5) + 5x * (-5 + 2x)) = 0
((25 + -10x) + 5x * (-5 + 2x)) = 0
(25 + -10x + (-5 * 5x + 2x * 5x)) = 0
(25 + -10x + (-25x + 10x2)) = 0

Combine like terms: -10x + -25x = -35x
(25 + -35x + 10x2) = 0

Solving
25 + -35x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(5 + -7x + 2x2) = 0

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

Ignore the factor 5.

Subproblem 1
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

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

Simplifying
5 + -2x = 0

Solving
5 + -2x = 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 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {1, 2.5}

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