x^3+8x^2+10x=2x^2+5x

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Solution for x^3+8x^2+10x=2x^2+5x equation: 


Simplifying
x3 + 8x2 + 10x = 2x2 + 5x

Reorder the terms:
10x + 8x2 + x3 = 2x2 + 5x

Reorder the terms:
10x + 8x2 + x3 = 5x + 2x2

Solving
10x + 8x2 + x3 = 5x + 2x2

Solving for variable 'x'.

Reorder the terms:
10x + -5x + 8x2 + -2x2 + x3 = 5x + 2x2 + -5x + -2x2

Combine like terms: 10x + -5x = 5x
5x + 8x2 + -2x2 + x3 = 5x + 2x2 + -5x + -2x2

Combine like terms: 8x2 + -2x2 = 6x2
5x + 6x2 + x3 = 5x + 2x2 + -5x + -2x2

Reorder the terms:
5x + 6x2 + x3 = 5x + -5x + 2x2 + -2x2

Combine like terms: 5x + -5x = 0
5x + 6x2 + x3 = 0 + 2x2 + -2x2
5x + 6x2 + x3 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
5x + 6x2 + x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(5 + 6x + x2) = 0

Factor a trinomial.
x((5 + x)(1 + x)) = 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 '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

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

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

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

Simplifying
x = -5

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

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

Simplifying
x = -1
Solution
x = {0, -5, -1}

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