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Simplifying [(3y2 + 11y + 4) + -1(-7y2 + 8y + 4)] + -1(6y2 + -10y + 12) = 0 Reorder the terms: [(4 + 11y + 3y2) + -1(-7y2 + 8y + 4)] + -1(6y2 + -10y + 12) = 0 Remove parenthesis around (4 + 11y + 3y2) [4 + 11y + 3y2 + -1(-7y2 + 8y + 4)] + -1(6y2 + -10y + 12) = 0 Reorder the terms: [4 + 11y + 3y2 + -1(4 + 8y + -7y2)] + -1(6y2 + -10y + 12) = 0 [4 + 11y + 3y2 + (4 * -1 + 8y * -1 + -7y2 * -1)] + -1(6y2 + -10y + 12) = 0 [4 + 11y + 3y2 + (-4 + -8y + 7y2)] + -1(6y2 + -10y + 12) = 0 Reorder the terms: [4 + -4 + 11y + -8y + 3y2 + 7y2] + -1(6y2 + -10y + 12) = 0 Combine like terms: 4 + -4 = 0 [0 + 11y + -8y + 3y2 + 7y2] + -1(6y2 + -10y + 12) = 0 [11y + -8y + 3y2 + 7y2] + -1(6y2 + -10y + 12) = 0 Combine like terms: 11y + -8y = 3y [3y + 3y2 + 7y2] + -1(6y2 + -10y + 12) = 0 Combine like terms: 3y2 + 7y2 = 10y2 [3y + 10y2] + -1(6y2 + -10y + 12) = 0 Remove brackets around [3y + 10y2] 3y + 10y2 + -1(6y2 + -10y + 12) = 0 Reorder the terms: 3y + 10y2 + -1(12 + -10y + 6y2) = 0 3y + 10y2 + (12 * -1 + -10y * -1 + 6y2 * -1) = 0 3y + 10y2 + (-12 + 10y + -6y2) = 0 Reorder the terms: -12 + 3y + 10y + 10y2 + -6y2 = 0 Combine like terms: 3y + 10y = 13y -12 + 13y + 10y2 + -6y2 = 0 Combine like terms: 10y2 + -6y2 = 4y2 -12 + 13y + 4y2 = 0 Solving -12 + 13y + 4y2 = 0 Solving for variable 'y'. Factor a trinomial. (-4 + -1y)(3 + -4y) = 0Subproblem 1
Set the factor '(-4 + -1y)' equal to zero and attempt to solve: Simplifying -4 + -1y = 0 Solving -4 + -1y = 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 + -1y = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1y = 0 + 4 -1y = 0 + 4 Combine like terms: 0 + 4 = 4 -1y = 4 Divide each side by '-1'. y = -4 Simplifying y = -4Subproblem 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 = {-4, 0.75}
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