y^4+7y^3+16y^2=0

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Solution for y^4+7y^3+16y^2=0 equation:


Simplifying
y4 + 7y3 + 16y2 = 0

Reorder the terms:
16y2 + 7y3 + y4 = 0

Solving
16y2 + 7y3 + y4 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y2'.
y2(16 + 7y + y2) = 0

Subproblem 1

Set the factor 'y2' equal to zero and attempt to solve: Simplifying y2 = 0 Solving y2 = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y2 = 0 Take the square root of each side: y = {0}

Subproblem 2

Set the factor '(16 + 7y + y2)' equal to zero and attempt to solve: Simplifying 16 + 7y + y2 = 0 Solving 16 + 7y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + 7y + -16 + y2 = 0 + -16 Reorder the terms: 16 + -16 + 7y + y2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + 7y + y2 = 0 + -16 7y + y2 = 0 + -16 Combine like terms: 0 + -16 = -16 7y + y2 = -16 The y term is 7y. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7y + 12.25 + y2 = -16 + 12.25 Reorder the terms: 12.25 + 7y + y2 = -16 + 12.25 Combine like terms: -16 + 12.25 = -3.75 12.25 + 7y + y2 = -3.75 Factor a perfect square on the left side: (y + 3.5)(y + 3.5) = -3.75 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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