(5x-20)(5x-10)=0

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Solution for (5x-20)(5x-10)=0 equation:


Simplifying
(5x + -20)(5x + -10) = 0

Reorder the terms:
(-20 + 5x)(5x + -10) = 0

Reorder the terms:
(-20 + 5x)(-10 + 5x) = 0

Multiply (-20 + 5x) * (-10 + 5x)
(-20(-10 + 5x) + 5x * (-10 + 5x)) = 0
((-10 * -20 + 5x * -20) + 5x * (-10 + 5x)) = 0
((200 + -100x) + 5x * (-10 + 5x)) = 0
(200 + -100x + (-10 * 5x + 5x * 5x)) = 0
(200 + -100x + (-50x + 25x2)) = 0

Combine like terms: -100x + -50x = -150x
(200 + -150x + 25x2) = 0

Solving
200 + -150x + 25x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '25'.
25(8 + -6x + x2) = 0

Factor a trinomial.
25((2 + -1x)(4 + -1x)) = 0

Ignore the factor 25.

Subproblem 1
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

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {2, 4}

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