(x^2+10x)(4x-40)=0

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Solution for (x^2+10x)(4x-40)=0 equation: 


Simplifying
(x2 + 10x)(4x + -40) = 0

Reorder the terms:
(10x + x2)(4x + -40) = 0

Reorder the terms:
(10x + x2)(-40 + 4x) = 0

Multiply (10x + x2) * (-40 + 4x)
(10x * (-40 + 4x) + x2(-40 + 4x)) = 0
((-40 * 10x + 4x * 10x) + x2(-40 + 4x)) = 0
((-400x + 40x2) + x2(-40 + 4x)) = 0
(-400x + 40x2 + (-40 * x2 + 4x * x2)) = 0
(-400x + 40x2 + (-40x2 + 4x3)) = 0

Combine like terms: 40x2 + -40x2 = 0
(-400x + 0 + 4x3) = 0
(-400x + 4x3) = 0

Solving
-400x + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-100 + x2) = 0

Factor a difference between two squares.
4x((10 + x)(-10 + x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(10 + x)' equal to zero and attempt to solve:

Simplifying
10 + x = 0

Solving
10 + x = 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 + x = 0 + -10

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

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

Simplifying
x = -10

Subproblem 3
Set the factor '(-10 + x)' equal to zero and attempt to solve:

Simplifying
-10 + x = 0

Solving
-10 + x = 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 + x = 0 + 10

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

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

Simplifying
x = 10
Solution
x = {0, -10, 10}

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