10x(x-4)+x(x^2-16)=

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Solution for 10x(x-4)+x(x^2-16)= equation: 


Simplifying
10x(x + -4) + x(x2 + -16) = 0

Reorder the terms:
10x(-4 + x) + x(x2 + -16) = 0
(-4 * 10x + x * 10x) + x(x2 + -16) = 0
(-40x + 10x2) + x(x2 + -16) = 0

Reorder the terms:
-40x + 10x2 + x(-16 + x2) = 0
-40x + 10x2 + (-16 * x + x2 * x) = 0
-40x + 10x2 + (-16x + x3) = 0

Reorder the terms:
-40x + -16x + 10x2 + x3 = 0

Combine like terms: -40x + -16x = -56x
-56x + 10x2 + x3 = 0

Solving
-56x + 10x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-56 + 10x + x2) = 0

Factor a trinomial.
x((-14 + -1x)(4 + -1x)) = 0


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 '(-14 + -1x)' equal to zero and attempt to solve:

Simplifying
-14 + -1x = 0

Solving
-14 + -1x = 0

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

Add '14' to each side of the equation.
-14 + 14 + -1x = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -1x = 0 + 14
-1x = 0 + 14

Combine like terms: 0 + 14 = 14
-1x = 14

Divide each side by '-1'.
x = -14

Simplifying
x = -14

Subproblem 3
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {0, -14, 4}

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