16x^3-16x^2+60x=0

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Solution for 16x^3-16x^2+60x=0 equation:


Simplifying
16x3 + -16x2 + 60x = 0

Reorder the terms:
60x + -16x2 + 16x3 = 0

Solving
60x + -16x2 + 16x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(15 + -4x + 4x2) = 0

Ignore the factor 4.

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 '(15 + -4x + 4x2)' equal to zero and attempt to solve: Simplifying 15 + -4x + 4x2 = 0 Solving 15 + -4x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3.75 + -1x + x2 = 0 Move the constant term to the right: Add '-3.75' to each side of the equation. 3.75 + -1x + -3.75 + x2 = 0 + -3.75 Reorder the terms: 3.75 + -3.75 + -1x + x2 = 0 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + -1x + x2 = 0 + -3.75 -1x + x2 = 0 + -3.75 Combine like terms: 0 + -3.75 = -3.75 -1x + x2 = -3.75 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = -3.75 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -3.75 + 0.25 Combine like terms: -3.75 + 0.25 = -3.5 0.25 + -1x + x2 = -3.5 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = -3.5 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Solution

x = {0}

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