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Simplifying (3a + -2)(4a + -4) = 0 Reorder the terms: (-2 + 3a)(4a + -4) = 0 Reorder the terms: (-2 + 3a)(-4 + 4a) = 0 Multiply (-2 + 3a) * (-4 + 4a) (-2(-4 + 4a) + 3a * (-4 + 4a)) = 0 ((-4 * -2 + 4a * -2) + 3a * (-4 + 4a)) = 0 ((8 + -8a) + 3a * (-4 + 4a)) = 0 (8 + -8a + (-4 * 3a + 4a * 3a)) = 0 (8 + -8a + (-12a + 12a2)) = 0 Combine like terms: -8a + -12a = -20a (8 + -20a + 12a2) = 0 Solving 8 + -20a + 12a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '4'. 4(2 + -5a + 3a2) = 0 Factor a trinomial. 4((2 + -3a)(1 + -1a)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(2 + -3a)' equal to zero and attempt to solve: Simplifying 2 + -3a = 0 Solving 2 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3a = 0 + -2 -3a = 0 + -2 Combine like terms: 0 + -2 = -2 -3a = -2 Divide each side by '-3'. a = 0.6666666667 Simplifying a = 0.6666666667Subproblem 2
Set the factor '(1 + -1a)' equal to zero and attempt to solve: Simplifying 1 + -1a = 0 Solving 1 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1a = 0 + -1 -1a = 0 + -1 Combine like terms: 0 + -1 = -1 -1a = -1 Divide each side by '-1'. a = 1 Simplifying a = 1Solution
a = {0.6666666667, 1}
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