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Simplifying 14y4 + -78y3 + 40y2 = 0 Reorder the terms: 40y2 + -78y3 + 14y4 = 0 Solving 40y2 + -78y3 + 14y4 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2y2'. 2y2(20 + -39y + 7y2) = 0 Factor a trinomial. 2y2((4 + -7y)(5 + -1y)) = 0 Ignore the factor 2.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 '(4 + -7y)' equal to zero and attempt to solve: Simplifying 4 + -7y = 0 Solving 4 + -7y = 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 + -7y = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -7y = 0 + -4 -7y = 0 + -4 Combine like terms: 0 + -4 = -4 -7y = -4 Divide each side by '-7'. y = 0.5714285714 Simplifying y = 0.5714285714Subproblem 3
Set the factor '(5 + -1y)' equal to zero and attempt to solve: Simplifying 5 + -1y = 0 Solving 5 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1y = 0 + -5 -1y = 0 + -5 Combine like terms: 0 + -5 = -5 -1y = -5 Divide each side by '-1'. y = 5 Simplifying y = 5Solution
y = {0, 0.5714285714, 5}
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