6x(3x+5)(8-x)=

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Solution for 6x(3x+5)(8-x)= equation: 


Simplifying
6x(3x + 5)(8 + -1x) = 0

Reorder the terms:
6x(5 + 3x)(8 + -1x) = 0

Multiply (5 + 3x) * (8 + -1x)
6x(5(8 + -1x) + 3x * (8 + -1x)) = 0
6x((8 * 5 + -1x * 5) + 3x * (8 + -1x)) = 0
6x((40 + -5x) + 3x * (8 + -1x)) = 0
6x(40 + -5x + (8 * 3x + -1x * 3x)) = 0
6x(40 + -5x + (24x + -3x2)) = 0

Combine like terms: -5x + 24x = 19x
6x(40 + 19x + -3x2) = 0
(40 * 6x + 19x * 6x + -3x2 * 6x) = 0
(240x + 114x2 + -18x3) = 0

Solving
240x + 114x2 + -18x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6x'.
6x(40 + 19x + -3x2) = 0

Factor a trinomial.
6x((8 + -1x)(5 + 3x)) = 0

Ignore the factor 6.

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

Simplifying
8 + -1x = 0

Solving
8 + -1x = 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 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8

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

Simplifying
5 + 3x = 0

Solving
5 + 3x = 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 + 3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3x = 0 + -5
3x = 0 + -5

Combine like terms: 0 + -5 = -5
3x = -5

Divide each side by '3'.
x = -1.666666667

Simplifying
x = -1.666666667
Solution
x = {0, 8, -1.666666667}

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