(3x^3-x^2)(48x-16)=0

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Solution for (3x^3-x^2)(48x-16)=0 equation: 


Simplifying
(3x3 + -1x2)(48x + -16) = 0

Reorder the terms:
(-1x2 + 3x3)(48x + -16) = 0

Reorder the terms:
(-1x2 + 3x3)(-16 + 48x) = 0

Multiply (-1x2 + 3x3) * (-16 + 48x)
(-1x2 * (-16 + 48x) + 3x3 * (-16 + 48x)) = 0
((-16 * -1x2 + 48x * -1x2) + 3x3 * (-16 + 48x)) = 0
((16x2 + -48x3) + 3x3 * (-16 + 48x)) = 0
(16x2 + -48x3 + (-16 * 3x3 + 48x * 3x3)) = 0
(16x2 + -48x3 + (-48x3 + 144x4)) = 0

Combine like terms: -48x3 + -48x3 = -96x3
(16x2 + -96x3 + 144x4) = 0

Solving
16x2 + -96x3 + 144x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '16x2'.
16x2(1 + -6x + 9x2) = 0

Factor a trinomial.
16x2((1 + -3x)(1 + -3x)) = 0

Ignore the factor 16.

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 '(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

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, 0.3333333333, 0.3333333333}

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