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Simplifying (-12a + 36)(15a + -4) = 0 Reorder the terms: (36 + -12a)(15a + -4) = 0 Reorder the terms: (36 + -12a)(-4 + 15a) = 0 Multiply (36 + -12a) * (-4 + 15a) (36(-4 + 15a) + -12a * (-4 + 15a)) = 0 ((-4 * 36 + 15a * 36) + -12a * (-4 + 15a)) = 0 ((-144 + 540a) + -12a * (-4 + 15a)) = 0 (-144 + 540a + (-4 * -12a + 15a * -12a)) = 0 (-144 + 540a + (48a + -180a2)) = 0 Combine like terms: 540a + 48a = 588a (-144 + 588a + -180a2) = 0 Solving -144 + 588a + -180a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '12'. 12(-12 + 49a + -15a2) = 0 Factor a trinomial. 12((-3 + a)(4 + -15a)) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(-3 + a)' equal to zero and attempt to solve: Simplifying -3 + a = 0 Solving -3 + a = 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 + a = 0 + 3 Combine like terms: -3 + 3 = 0 0 + a = 0 + 3 a = 0 + 3 Combine like terms: 0 + 3 = 3 a = 3 Simplifying a = 3Subproblem 2
Set the factor '(4 + -15a)' equal to zero and attempt to solve: Simplifying 4 + -15a = 0 Solving 4 + -15a = 0 Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -15a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -15a = 0 + -4 -15a = 0 + -4 Combine like terms: 0 + -4 = -4 -15a = -4 Divide each side by '-15'. a = 0.2666666667 Simplifying a = 0.2666666667Solution
a = {3, 0.2666666667}
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