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Simplifying -5y(4y + -3) + 2 = -20y + 17 Reorder the terms: -5y(-3 + 4y) + 2 = -20y + 17 (-3 * -5y + 4y * -5y) + 2 = -20y + 17 (15y + -20y2) + 2 = -20y + 17 Reorder the terms: 2 + 15y + -20y2 = -20y + 17 Reorder the terms: 2 + 15y + -20y2 = 17 + -20y Solving 2 + 15y + -20y2 = 17 + -20y Solving for variable 'y'. Reorder the terms: 2 + -17 + 15y + 20y + -20y2 = 17 + -20y + -17 + 20y Combine like terms: 2 + -17 = -15 -15 + 15y + 20y + -20y2 = 17 + -20y + -17 + 20y Combine like terms: 15y + 20y = 35y -15 + 35y + -20y2 = 17 + -20y + -17 + 20y Reorder the terms: -15 + 35y + -20y2 = 17 + -17 + -20y + 20y Combine like terms: 17 + -17 = 0 -15 + 35y + -20y2 = 0 + -20y + 20y -15 + 35y + -20y2 = -20y + 20y Combine like terms: -20y + 20y = 0 -15 + 35y + -20y2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-3 + 7y + -4y2) = 0 Factor a trinomial. 5((-1 + y)(3 + -4y)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-1 + y)' equal to zero and attempt to solve: Simplifying -1 + y = 0 Solving -1 + y = 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 + y = 0 + 1 Combine like terms: -1 + 1 = 0 0 + y = 0 + 1 y = 0 + 1 Combine like terms: 0 + 1 = 1 y = 1 Simplifying y = 1Subproblem 2
Set the factor '(3 + -4y)' equal to zero and attempt to solve: Simplifying 3 + -4y = 0 Solving 3 + -4y = 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 + -4y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4y = 0 + -3 -4y = 0 + -3 Combine like terms: 0 + -3 = -3 -4y = -3 Divide each side by '-4'. y = 0.75 Simplifying y = 0.75Solution
y = {1, 0.75}
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