4y^3-5y^2+20y=0

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Solution for 4y^3-5y^2+20y=0 equation:


Simplifying
4y3 + -5y2 + 20y = 0

Reorder the terms:
20y + -5y2 + 4y3 = 0

Solving
20y + -5y2 + 4y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(20 + -5y + 4y2) = 0

Subproblem 1

Set the factor 'y' equal to zero and attempt to solve: Simplifying y = 0 Solving y = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y = 0

Subproblem 2

Set the factor '(20 + -5y + 4y2)' equal to zero and attempt to solve: Simplifying 20 + -5y + 4y2 = 0 Solving 20 + -5y + 4y2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 5 + -1.25y + y2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -1.25y + -5 + y2 = 0 + -5 Reorder the terms: 5 + -5 + -1.25y + y2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1.25y + y2 = 0 + -5 -1.25y + y2 = 0 + -5 Combine like terms: 0 + -5 = -5 -1.25y + y2 = -5 The y term is -1.25y. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25y + 0.390625 + y2 = -5 + 0.390625 Reorder the terms: 0.390625 + -1.25y + y2 = -5 + 0.390625 Combine like terms: -5 + 0.390625 = -4.609375 0.390625 + -1.25y + y2 = -4.609375 Factor a perfect square on the left side: (y + -0.625)(y + -0.625) = -4.609375 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

y = {0}

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