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Simplifying y4 + 12y3 + -64y2 = 0 Reorder the terms: -64y2 + 12y3 + y4 = 0 Solving -64y2 + 12y3 + y4 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y2'. y2(-64 + 12y + y2) = 0 Factor a trinomial. y2((-16 + -1y)(4 + -1y)) = 0Subproblem 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 + -1y)' equal to zero and attempt to solve: Simplifying -16 + -1y = 0 Solving -16 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + -1y = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -1y = 0 + 16 -1y = 0 + 16 Combine like terms: 0 + 16 = 16 -1y = 16 Divide each side by '-1'. y = -16 Simplifying y = -16Subproblem 3
Set the factor '(4 + -1y)' equal to zero and attempt to solve: Simplifying 4 + -1y = 0 Solving 4 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1y = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1y = 0 + -4 -1y = 0 + -4 Combine like terms: 0 + -4 = -4 -1y = -4 Divide each side by '-1'. y = 4 Simplifying y = 4Solution
y = {0, -16, 4}
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