(8x^3-3x^2+6x)+(7x^3+7x^2-10x)=

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Solution for (8x^3-3x^2+6x)+(7x^3+7x^2-10x)= equation: 


Simplifying
(8x3 + -3x2 + 6x) + (7x3 + 7x2 + -10x) = 0

Reorder the terms:
(6x + -3x2 + 8x3) + (7x3 + 7x2 + -10x) = 0

Remove parenthesis around (6x + -3x2 + 8x3)
6x + -3x2 + 8x3 + (7x3 + 7x2 + -10x) = 0

Reorder the terms:
6x + -3x2 + 8x3 + (-10x + 7x2 + 7x3) = 0

Remove parenthesis around (-10x + 7x2 + 7x3)
6x + -3x2 + 8x3 + -10x + 7x2 + 7x3 = 0

Reorder the terms:
6x + -10x + -3x2 + 7x2 + 8x3 + 7x3 = 0

Combine like terms: 6x + -10x = -4x
-4x + -3x2 + 7x2 + 8x3 + 7x3 = 0

Combine like terms: -3x2 + 7x2 = 4x2
-4x + 4x2 + 8x3 + 7x3 = 0

Combine like terms: 8x3 + 7x3 = 15x3
-4x + 4x2 + 15x3 = 0

Solving
-4x + 4x2 + 15x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-4 + 4x + 15x2) = 0

Factor a trinomial.
x((-2 + -3x)(2 + -5x)) = 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 '(-2 + -3x)' equal to zero and attempt to solve:

Simplifying
-2 + -3x = 0

Solving
-2 + -3x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -3x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3x = 0 + 2
-3x = 0 + 2

Combine like terms: 0 + 2 = 2
-3x = 2

Divide each side by '-3'.
x = -0.6666666667

Simplifying
x = -0.6666666667

Subproblem 3
Set the factor '(2 + -5x)' equal to zero and attempt to solve:

Simplifying
2 + -5x = 0

Solving
2 + -5x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -5x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5x = 0 + -2
-5x = 0 + -2

Combine like terms: 0 + -2 = -2
-5x = -2

Divide each side by '-5'.
x = 0.4

Simplifying
x = 0.4
Solution
x = {0, -0.6666666667, 0.4}

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