(5x-10)(5x-5)=0

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Solution for (5x-10)(5x-5)=0 equation: 


Simplifying
(5x + -10)(5x + -5) = 0

Reorder the terms:
(-10 + 5x)(5x + -5) = 0

Reorder the terms:
(-10 + 5x)(-5 + 5x) = 0

Multiply (-10 + 5x) * (-5 + 5x)
(-10(-5 + 5x) + 5x * (-5 + 5x)) = 0
((-5 * -10 + 5x * -10) + 5x * (-5 + 5x)) = 0
((50 + -50x) + 5x * (-5 + 5x)) = 0
(50 + -50x + (-5 * 5x + 5x * 5x)) = 0
(50 + -50x + (-25x + 25x2)) = 0

Combine like terms: -50x + -25x = -75x
(50 + -75x + 25x2) = 0

Solving
50 + -75x + 25x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '25'.
25(2 + -3x + x2) = 0

Factor a trinomial.
25((1 + -1x)(2 + -1x)) = 0

Ignore the factor 25.

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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {1, 2}

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