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

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


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

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

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

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

Combine like terms: -5x + 10x = 5x
5(-50 + 5x + x2) = 0
(-50 * 5 + 5x * 5 + x2 * 5) = 0
(-250 + 25x + 5x2) = 0

Solving
-250 + 25x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-50 + 5x + x2) = 0

Factor a trinomial.
5((-10 + -1x)(5 + -1x)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-10 + -1x)' equal to zero and attempt to solve:

Simplifying
-10 + -1x = 0

Solving
-10 + -1x = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1x = 0 + 10
-1x = 0 + 10

Combine like terms: 0 + 10 = 10
-1x = 10

Divide each side by '-1'.
x = -10

Simplifying
x = -10

Subproblem 2
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
Solution
x = {-10, 5}

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