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Simplifying -4a(3a + -4) + -2(a + -3a) = 0 Reorder the terms: -4a(-4 + 3a) + -2(a + -3a) = 0 (-4 * -4a + 3a * -4a) + -2(a + -3a) = 0 (16a + -12a2) + -2(a + -3a) = 0 Combine like terms: a + -3a = -2a 16a + -12a2 + -2(-2a) = 0 Remove parenthesis around (-2a) 16a + -12a2 + -2 * -2a = 0 Multiply -2 * -2 16a + -12a2 + 4a = 0 Reorder the terms: 16a + 4a + -12a2 = 0 Combine like terms: 16a + 4a = 20a 20a + -12a2 = 0 Solving 20a + -12a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '4a'. 4a(5 + -3a) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 2
Set the factor '(5 + -3a)' equal to zero and attempt to solve: Simplifying 5 + -3a = 0 Solving 5 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -3a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3a = 0 + -5 -3a = 0 + -5 Combine like terms: 0 + -5 = -5 -3a = -5 Divide each side by '-3'. a = 1.666666667 Simplifying a = 1.666666667Solution
a = {0, 1.666666667}
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