6x^2(x+8)+5x(x+8)=0

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Solution for 6x^2(x+8)+5x(x+8)=0 equation: 


Simplifying
6x2(x + 8) + 5x(x + 8) = 0

Reorder the terms:
6x2(8 + x) + 5x(x + 8) = 0
(8 * 6x2 + x * 6x2) + 5x(x + 8) = 0
(48x2 + 6x3) + 5x(x + 8) = 0

Reorder the terms:
48x2 + 6x3 + 5x(8 + x) = 0
48x2 + 6x3 + (8 * 5x + x * 5x) = 0
48x2 + 6x3 + (40x + 5x2) = 0

Reorder the terms:
40x + 48x2 + 5x2 + 6x3 = 0

Combine like terms: 48x2 + 5x2 = 53x2
40x + 53x2 + 6x3 = 0

Solving
40x + 53x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(40 + 53x + 6x2) = 0

Factor a trinomial.
x((8 + x)(5 + 6x)) = 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 '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 0

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

Add '-8' to each side of the equation.
8 + -8 + x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x = 0 + -8
x = 0 + -8

Combine like terms: 0 + -8 = -8
x = -8

Simplifying
x = -8

Subproblem 3
Set the factor '(5 + 6x)' equal to zero and attempt to solve:

Simplifying
5 + 6x = 0

Solving
5 + 6x = 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 + 6x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 6x = 0 + -5
6x = 0 + -5

Combine like terms: 0 + -5 = -5
6x = -5

Divide each side by '6'.
x = -0.8333333333

Simplifying
x = -0.8333333333
Solution
x = {0, -8, -0.8333333333}

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