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Simplifying 5y4(3y2 + -12y)(y + -4) = 0 Reorder the terms: 5y4(-12y + 3y2)(y + -4) = 0 Reorder the terms: 5y4(-12y + 3y2)(-4 + y) = 0 Multiply (-12y + 3y2) * (-4 + y) 5y4(-12y * (-4 + y) + 3y2 * (-4 + y)) = 0 5y4((-4 * -12y + y * -12y) + 3y2 * (-4 + y)) = 0 5y4((48y + -12y2) + 3y2 * (-4 + y)) = 0 5y4(48y + -12y2 + (-4 * 3y2 + y * 3y2)) = 0 5y4(48y + -12y2 + (-12y2 + 3y3)) = 0 Combine like terms: -12y2 + -12y2 = -24y2 5y4(48y + -24y2 + 3y3) = 0 (48y * 5y4 + -24y2 * 5y4 + 3y3 * 5y4) = 0 (240y5 + -120y6 + 15y7) = 0 Solving 240y5 + -120y6 + 15y7 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '15y5'. 15y5(16 + -8y + y2) = 0 Factor a trinomial. 15y5((4 + -1y)(4 + -1y)) = 0 Ignore the factor 15.Subproblem 1
Set the factor 'y5' equal to zero and attempt to solve: Simplifying y5 = 0 Solving y5 = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y5 = 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 '(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 = 4Subproblem 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 = {4, 4}
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