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Simplifying (2a + -3)(4a + 6a + 9) = 0 Reorder the terms: (-3 + 2a)(4a + 6a + 9) = 0 Reorder the terms: (-3 + 2a)(9 + 4a + 6a) = 0 Combine like terms: 4a + 6a = 10a (-3 + 2a)(9 + 10a) = 0 Multiply (-3 + 2a) * (9 + 10a) (-3(9 + 10a) + 2a * (9 + 10a)) = 0 ((9 * -3 + 10a * -3) + 2a * (9 + 10a)) = 0 ((-27 + -30a) + 2a * (9 + 10a)) = 0 (-27 + -30a + (9 * 2a + 10a * 2a)) = 0 (-27 + -30a + (18a + 20a2)) = 0 Combine like terms: -30a + 18a = -12a (-27 + -12a + 20a2) = 0 Solving -27 + -12a + 20a2 = 0 Solving for variable 'a'. Factor a trinomial. (-9 + -10a)(3 + -2a) = 0Subproblem 1
Set the factor '(-9 + -10a)' equal to zero and attempt to solve: Simplifying -9 + -10a = 0 Solving -9 + -10a = 0 Move all terms containing a to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -10a = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -10a = 0 + 9 -10a = 0 + 9 Combine like terms: 0 + 9 = 9 -10a = 9 Divide each side by '-10'. a = -0.9 Simplifying a = -0.9Subproblem 2
Set the factor '(3 + -2a)' equal to zero and attempt to solve: Simplifying 3 + -2a = 0 Solving 3 + -2a = 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 + -2a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2a = 0 + -3 -2a = 0 + -3 Combine like terms: 0 + -3 = -3 -2a = -3 Divide each side by '-2'. a = 1.5 Simplifying a = 1.5Solution
a = {-0.9, 1.5}
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