(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 = -80x2
(-400x + -80x2 + -4x3) = 0

Solving
-400x + -80x2 + -4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-4x'.
-4x(100 + 20x + x2) = 0

Factor a trinomial.
-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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