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Simplifying (3y + 9)(y + -7) = 0 Reorder the terms: (9 + 3y)(y + -7) = 0 Reorder the terms: (9 + 3y)(-7 + y) = 0 Multiply (9 + 3y) * (-7 + y) (9(-7 + y) + 3y * (-7 + y)) = 0 ((-7 * 9 + y * 9) + 3y * (-7 + y)) = 0 ((-63 + 9y) + 3y * (-7 + y)) = 0 (-63 + 9y + (-7 * 3y + y * 3y)) = 0 (-63 + 9y + (-21y + 3y2)) = 0 Combine like terms: 9y + -21y = -12y (-63 + -12y + 3y2) = 0 Solving -63 + -12y + 3y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '3'. 3(-21 + -4y + y2) = 0 Factor a trinomial. 3((-3 + -1y)(7 + -1y)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3 + -1y)' equal to zero and attempt to solve: Simplifying -3 + -1y = 0 Solving -3 + -1y = 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 + -1y = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1y = 0 + 3 -1y = 0 + 3 Combine like terms: 0 + 3 = 3 -1y = 3 Divide each side by '-1'. y = -3 Simplifying y = -3Subproblem 2
Set the factor '(7 + -1y)' equal to zero and attempt to solve: Simplifying 7 + -1y = 0 Solving 7 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1y = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1y = 0 + -7 -1y = 0 + -7 Combine like terms: 0 + -7 = -7 -1y = -7 Divide each side by '-1'. y = 7 Simplifying y = 7Solution
y = {-3, 7}
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