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Simplifying 0 = (3ab + 9)(3ab + 7) Reorder the terms: 0 = (9 + 3ab)(3ab + 7) Reorder the terms: 0 = (9 + 3ab)(7 + 3ab) Multiply (9 + 3ab) * (7 + 3ab) 0 = (9(7 + 3ab) + 3ab * (7 + 3ab)) 0 = ((7 * 9 + 3ab * 9) + 3ab * (7 + 3ab)) 0 = ((63 + 27ab) + 3ab * (7 + 3ab)) 0 = (63 + 27ab + (7 * 3ab + 3ab * 3ab)) 0 = (63 + 27ab + (21ab + 9a2b2)) Combine like terms: 27ab + 21ab = 48ab 0 = (63 + 48ab + 9a2b2) Solving 0 = 63 + 48ab + 9a2b2 Solving for variable 'a'. Combine like terms: 0 + -63 = -63 -63 + -48ab + -9a2b2 = 63 + 48ab + 9a2b2 + -63 + -48ab + -9a2b2 Reorder the terms: -63 + -48ab + -9a2b2 = 63 + -63 + 48ab + -48ab + 9a2b2 + -9a2b2 Combine like terms: 63 + -63 = 0 -63 + -48ab + -9a2b2 = 0 + 48ab + -48ab + 9a2b2 + -9a2b2 -63 + -48ab + -9a2b2 = 48ab + -48ab + 9a2b2 + -9a2b2 Combine like terms: 48ab + -48ab = 0 -63 + -48ab + -9a2b2 = 0 + 9a2b2 + -9a2b2 -63 + -48ab + -9a2b2 = 9a2b2 + -9a2b2 Combine like terms: 9a2b2 + -9a2b2 = 0 -63 + -48ab + -9a2b2 = 0 Factor out the Greatest Common Factor (GCF), '-3'. -3(21 + 16ab + 3a2b2) = 0 Factor a trinomial. -3((3 + ab)(7 + 3ab)) = 0 Ignore the factor -3.Subproblem 1
Set the factor '(3 + ab)' equal to zero and attempt to solve: Simplifying 3 + ab = 0 Solving 3 + ab = 0 Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + ab = 0 + -3 Combine like terms: 3 + -3 = 0 0 + ab = 0 + -3 ab = 0 + -3 Combine like terms: 0 + -3 = -3 ab = -3 Divide each side by 'b'. a = -3b-1 Simplifying a = -3b-1Subproblem 2
Set the factor '(7 + 3ab)' equal to zero and attempt to solve: Simplifying 7 + 3ab = 0 Solving 7 + 3ab = 0 Move all terms containing a to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 3ab = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 3ab = 0 + -7 3ab = 0 + -7 Combine like terms: 0 + -7 = -7 3ab = -7 Divide each side by '3b'. a = -2.333333333b-1 Simplifying a = -2.333333333b-1Solution
a = {-3b-1, -2.333333333b-1}
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