(2x-5)(2x+10)=0

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Solution for (2x-5)(2x+10)=0 equation: 


Simplifying
(2x + -5)(2x + 10) = 0

Reorder the terms:
(-5 + 2x)(2x + 10) = 0

Reorder the terms:
(-5 + 2x)(10 + 2x) = 0

Multiply (-5 + 2x) * (10 + 2x)
(-5(10 + 2x) + 2x * (10 + 2x)) = 0
((10 * -5 + 2x * -5) + 2x * (10 + 2x)) = 0
((-50 + -10x) + 2x * (10 + 2x)) = 0
(-50 + -10x + (10 * 2x + 2x * 2x)) = 0
(-50 + -10x + (20x + 4x2)) = 0

Combine like terms: -10x + 20x = 10x
(-50 + 10x + 4x2) = 0

Solving
-50 + 10x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-25 + 5x + 2x2) = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 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 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5

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 = {-5, 2.5}

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