(x+20)(8x+10)x=

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Solution for (x+20)(8x+10)x= equation: 


Simplifying
(x + 20)(8x + 10) * x = 0

Reorder the terms:
(20 + x)(8x + 10) * x = 0

Reorder the terms:
(20 + x)(10 + 8x) * x = 0

Reorder the terms for easier multiplication:
x(20 + x)(10 + 8x) = 0

Multiply (20 + x) * (10 + 8x)
x(20(10 + 8x) + x(10 + 8x)) = 0
x((10 * 20 + 8x * 20) + x(10 + 8x)) = 0
x((200 + 160x) + x(10 + 8x)) = 0
x(200 + 160x + (10 * x + 8x * x)) = 0
x(200 + 160x + (10x + 8x2)) = 0

Combine like terms: 160x + 10x = 170x
x(200 + 170x + 8x2) = 0
(200 * x + 170x * x + 8x2 * x) = 0
(200x + 170x2 + 8x3) = 0

Solving
200x + 170x2 + 8x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(100 + 85x + 4x2) = 0

Factor a trinomial.
2x((20 + x)(5 + 4x)) = 0

Ignore the factor 2.

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 '(20 + x)' equal to zero and attempt to solve:

Simplifying
20 + x = 0

Solving
20 + x = 0

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

Add '-20' to each side of the equation.
20 + -20 + x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + x = 0 + -20
x = 0 + -20

Combine like terms: 0 + -20 = -20
x = -20

Simplifying
x = -20

Subproblem 3
Set the factor '(5 + 4x)' equal to zero and attempt to solve:

Simplifying
5 + 4x = 0

Solving
5 + 4x = 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 + 4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4x = 0 + -5
4x = 0 + -5

Combine like terms: 0 + -5 = -5
4x = -5

Divide each side by '4'.
x = -1.25

Simplifying
x = -1.25
Solution
x = {0, -20, -1.25}

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