32x^3-16x^2=4x^2

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Solution for 32x^3-16x^2=4x^2 equation:


Simplifying
32x3 + -16x2 = 4x2

Reorder the terms:
-16x2 + 32x3 = 4x2

Solving
-16x2 + 32x3 = 4x2

Solving for variable 'x'.

Reorder the terms:
-16x2 + -4x2 + 32x3 = 4x2 + -4x2

Combine like terms: -16x2 + -4x2 = -20x2
-20x2 + 32x3 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-20x2 + 32x3 = 0

Factor out the Greatest Common Factor (GCF), '4x2'.
4x2(-5 + 8x) = 0

Ignore the factor 4.

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 '(-5 + 8x)' equal to zero and attempt to solve: Simplifying -5 + 8x = 0 Solving -5 + 8x = 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 + 8x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 8x = 0 + 5 8x = 0 + 5 Combine like terms: 0 + 5 = 5 8x = 5 Divide each side by '8'. x = 0.625 Simplifying x = 0.625

Solution

x = {0, 0.625}

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