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Simplifying 10y3 + -4y2 + -2y = -5y3 + 3y2 Reorder the terms: -2y + -4y2 + 10y3 = -5y3 + 3y2 Reorder the terms: -2y + -4y2 + 10y3 = 3y2 + -5y3 Solving -2y + -4y2 + 10y3 = 3y2 + -5y3 Solving for variable 'y'. Reorder the terms: -2y + -4y2 + -3y2 + 10y3 + 5y3 = 3y2 + -5y3 + -3y2 + 5y3 Combine like terms: -4y2 + -3y2 = -7y2 -2y + -7y2 + 10y3 + 5y3 = 3y2 + -5y3 + -3y2 + 5y3 Combine like terms: 10y3 + 5y3 = 15y3 -2y + -7y2 + 15y3 = 3y2 + -5y3 + -3y2 + 5y3 Reorder the terms: -2y + -7y2 + 15y3 = 3y2 + -3y2 + -5y3 + 5y3 Combine like terms: 3y2 + -3y2 = 0 -2y + -7y2 + 15y3 = 0 + -5y3 + 5y3 -2y + -7y2 + 15y3 = -5y3 + 5y3 Combine like terms: -5y3 + 5y3 = 0 -2y + -7y2 + 15y3 = 0 Factor out the Greatest Common Factor (GCF), 'y'. y(-2 + -7y + 15y2) = 0 Factor a trinomial. y((-1 + -5y)(2 + -3y)) = 0Subproblem 1
Set the factor 'y' equal to zero and attempt to solve: Simplifying y = 0 Solving y = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y = 0Subproblem 2
Set the factor '(-1 + -5y)' equal to zero and attempt to solve: Simplifying -1 + -5y = 0 Solving -1 + -5y = 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 + -5y = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -5y = 0 + 1 -5y = 0 + 1 Combine like terms: 0 + 1 = 1 -5y = 1 Divide each side by '-5'. y = -0.2 Simplifying y = -0.2Subproblem 3
Set the factor '(2 + -3y)' equal to zero and attempt to solve: Simplifying 2 + -3y = 0 Solving 2 + -3y = 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 + -3y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3y = 0 + -2 -3y = 0 + -2 Combine like terms: 0 + -2 = -2 -3y = -2 Divide each side by '-3'. y = 0.6666666667 Simplifying y = 0.6666666667Solution
y = {0, -0.2, 0.6666666667}
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