(x^2-3x^3)(8x-24)=

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Solution for (x^2-3x^3)(8x-24)= equation: 


Simplifying
(x2 + -3x3)(8x + -24) = 0

Reorder the terms:
(x2 + -3x3)(-24 + 8x) = 0

Multiply (x2 + -3x3) * (-24 + 8x)
(x2(-24 + 8x) + -3x3 * (-24 + 8x)) = 0
((-24 * x2 + 8x * x2) + -3x3 * (-24 + 8x)) = 0
((-24x2 + 8x3) + -3x3 * (-24 + 8x)) = 0
(-24x2 + 8x3 + (-24 * -3x3 + 8x * -3x3)) = 0
(-24x2 + 8x3 + (72x3 + -24x4)) = 0

Combine like terms: 8x3 + 72x3 = 80x3
(-24x2 + 80x3 + -24x4) = 0

Solving
-24x2 + 80x3 + -24x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8x2'.
8x2(-3 + 10x + -3x2) = 0

Factor a trinomial.
8x2((-3 + x)(1 + -3x)) = 0

Ignore the factor 8.

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

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

Simplifying
-3 + x = 0

Solving
-3 + x = 0

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

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

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

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

Simplifying
x = 3

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

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {0, 3, 0.3333333333}

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