-3x(3x+8)(x-5)=0

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Solution for -3x(3x+8)(x-5)=0 equation: 


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

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

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

Multiply (8 + 3x) * (-5 + x)
-3x(8(-5 + x) + 3x * (-5 + x)) = 0
-3x((-5 * 8 + x * 8) + 3x * (-5 + x)) = 0
-3x((-40 + 8x) + 3x * (-5 + x)) = 0
-3x(-40 + 8x + (-5 * 3x + x * 3x)) = 0
-3x(-40 + 8x + (-15x + 3x2)) = 0

Combine like terms: 8x + -15x = -7x
-3x(-40 + -7x + 3x2) = 0
(-40 * -3x + -7x * -3x + 3x2 * -3x) = 0
(120x + 21x2 + -9x3) = 0

Solving
120x + 21x2 + -9x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(40 + 7x + -3x2) = 0

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

Ignore the factor 3.

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

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5

Subproblem 3
Set the factor '(8 + 3x)' equal to zero and attempt to solve:

Simplifying
8 + 3x = 0

Solving
8 + 3x = 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 + 3x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 3x = 0 + -8
3x = 0 + -8

Combine like terms: 0 + -8 = -8
3x = -8

Divide each side by '3'.
x = -2.666666667

Simplifying
x = -2.666666667
Solution
x = {0, 5, -2.666666667}

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