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Simplifying 6y2 + 11y + -10 = (2y + 5) Reorder the terms: -10 + 11y + 6y2 = (2y + 5) Reorder the terms: -10 + 11y + 6y2 = (5 + 2y) Remove parenthesis around (5 + 2y) -10 + 11y + 6y2 = 5 + 2y Solving -10 + 11y + 6y2 = 5 + 2y Solving for variable 'y'. Reorder the terms: -10 + -5 + 11y + -2y + 6y2 = 5 + 2y + -5 + -2y Combine like terms: -10 + -5 = -15 -15 + 11y + -2y + 6y2 = 5 + 2y + -5 + -2y Combine like terms: 11y + -2y = 9y -15 + 9y + 6y2 = 5 + 2y + -5 + -2y Reorder the terms: -15 + 9y + 6y2 = 5 + -5 + 2y + -2y Combine like terms: 5 + -5 = 0 -15 + 9y + 6y2 = 0 + 2y + -2y -15 + 9y + 6y2 = 2y + -2y Combine like terms: 2y + -2y = 0 -15 + 9y + 6y2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + 3y + 2y2) = 0 Factor a trinomial. 3((-5 + -2y)(1 + -1y)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + -2y)' equal to zero and attempt to solve: Simplifying -5 + -2y = 0 Solving -5 + -2y = 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 + -2y = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2y = 0 + 5 -2y = 0 + 5 Combine like terms: 0 + 5 = 5 -2y = 5 Divide each side by '-2'. y = -2.5 Simplifying y = -2.5Subproblem 2
Set the factor '(1 + -1y)' equal to zero and attempt to solve: Simplifying 1 + -1y = 0 Solving 1 + -1y = 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 + -1y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1y = 0 + -1 -1y = 0 + -1 Combine like terms: 0 + -1 = -1 -1y = -1 Divide each side by '-1'. y = 1 Simplifying y = 1Solution
y = {-2.5, 1}
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