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Simplifying 4y3(4y + 1)(y + -4) = 0 Reorder the terms: 4y3(1 + 4y)(y + -4) = 0 Reorder the terms: 4y3(1 + 4y)(-4 + y) = 0 Multiply (1 + 4y) * (-4 + y) 4y3(1(-4 + y) + 4y * (-4 + y)) = 0 4y3((-4 * 1 + y * 1) + 4y * (-4 + y)) = 0 4y3((-4 + 1y) + 4y * (-4 + y)) = 0 4y3(-4 + 1y + (-4 * 4y + y * 4y)) = 0 4y3(-4 + 1y + (-16y + 4y2)) = 0 Combine like terms: 1y + -16y = -15y 4y3(-4 + -15y + 4y2) = 0 (-4 * 4y3 + -15y * 4y3 + 4y2 * 4y3) = 0 (-16y3 + -60y4 + 16y5) = 0 Solving -16y3 + -60y4 + 16y5 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '4y3'. 4y3(-4 + -15y + 4y2) = 0 Factor a trinomial. 4y3((-1 + -4y)(4 + -1y)) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'y3' equal to zero and attempt to solve: Simplifying y3 = 0 Solving y3 = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-1 + -4y)' equal to zero and attempt to solve: Simplifying -1 + -4y = 0 Solving -1 + -4y = 0 Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -4y = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4y = 0 + 1 -4y = 0 + 1 Combine like terms: 0 + 1 = 1 -4y = 1 Divide each side by '-4'. y = -0.25 Simplifying y = -0.25Subproblem 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 = {-0.25, 4}
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