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Simplifying (10y2 + -8y + 9) + -1(4y2 + 4y + 3) = 0 Reorder the terms: (9 + -8y + 10y2) + -1(4y2 + 4y + 3) = 0 Remove parenthesis around (9 + -8y + 10y2) 9 + -8y + 10y2 + -1(4y2 + 4y + 3) = 0 Reorder the terms: 9 + -8y + 10y2 + -1(3 + 4y + 4y2) = 0 9 + -8y + 10y2 + (3 * -1 + 4y * -1 + 4y2 * -1) = 0 9 + -8y + 10y2 + (-3 + -4y + -4y2) = 0 Reorder the terms: 9 + -3 + -8y + -4y + 10y2 + -4y2 = 0 Combine like terms: 9 + -3 = 6 6 + -8y + -4y + 10y2 + -4y2 = 0 Combine like terms: -8y + -4y = -12y 6 + -12y + 10y2 + -4y2 = 0 Combine like terms: 10y2 + -4y2 = 6y2 6 + -12y + 6y2 = 0 Solving 6 + -12y + 6y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '6'. 6(1 + -2y + y2) = 0 Factor a trinomial. 6((1 + -1y)(1 + -1y)) = 0 Ignore the factor 6.Subproblem 1
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 = 1Subproblem 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 = {1, 1}
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