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

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Solution for 4(x+10)(x-5)=0 equation: 


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

Reorder the terms:
4(10 + x)(x + -5) = 0

Reorder the terms:
4(10 + x)(-5 + x) = 0

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

Combine like terms: 10x + -5x = 5x
4(-50 + 5x + x2) = 0
(-50 * 4 + 5x * 4 + x2 * 4) = 0
(-200 + 20x + 4x2) = 0

Solving
-200 + 20x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-50 + 5x + x2) = 0

Factor a trinomial.
4((-10 + -1x)(5 + -1x)) = 0

Ignore the factor 4.

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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