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Simplifying 2y2(5y + 3)(y + -2) = 0 Reorder the terms: 2y2(3 + 5y)(y + -2) = 0 Reorder the terms: 2y2(3 + 5y)(-2 + y) = 0 Multiply (3 + 5y) * (-2 + y) 2y2(3(-2 + y) + 5y * (-2 + y)) = 0 2y2((-2 * 3 + y * 3) + 5y * (-2 + y)) = 0 2y2((-6 + 3y) + 5y * (-2 + y)) = 0 2y2(-6 + 3y + (-2 * 5y + y * 5y)) = 0 2y2(-6 + 3y + (-10y + 5y2)) = 0 Combine like terms: 3y + -10y = -7y 2y2(-6 + -7y + 5y2) = 0 (-6 * 2y2 + -7y * 2y2 + 5y2 * 2y2) = 0 (-12y2 + -14y3 + 10y4) = 0 Solving -12y2 + -14y3 + 10y4 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2y2'. 2y2(-6 + -7y + 5y2) = 0 Factor a trinomial. 2y2((-3 + -5y)(2 + -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 '(-3 + -5y)' equal to zero and attempt to solve: Simplifying -3 + -5y = 0 Solving -3 + -5y = 0 Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -5y = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -5y = 0 + 3 -5y = 0 + 3 Combine like terms: 0 + 3 = 3 -5y = 3 Divide each side by '-5'. y = -0.6 Simplifying y = -0.6Subproblem 3
Set the factor '(2 + -1y)' equal to zero and attempt to solve: Simplifying 2 + -1y = 0 Solving 2 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1y = 0 + -2 -1y = 0 + -2 Combine like terms: 0 + -2 = -2 -1y = -2 Divide each side by '-1'. y = 2 Simplifying y = 2Solution
y = {0, -0.6, 2}
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