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Simplifying 20a2 = -12a + 8 Reorder the terms: 20a2 = 8 + -12a Solving 20a2 = 8 + -12a Solving for variable 'a'. Reorder the terms: -8 + 12a + 20a2 = 8 + -12a + -8 + 12a Reorder the terms: -8 + 12a + 20a2 = 8 + -8 + -12a + 12a Combine like terms: 8 + -8 = 0 -8 + 12a + 20a2 = 0 + -12a + 12a -8 + 12a + 20a2 = -12a + 12a Combine like terms: -12a + 12a = 0 -8 + 12a + 20a2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-2 + 3a + 5a2) = 0 Factor a trinomial. 4((-1 + -1a)(2 + -5a)) = 0 Ignore the factor 4.Subproblem 1
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 = -1Subproblem 2
Set the factor '(2 + -5a)' equal to zero and attempt to solve: Simplifying 2 + -5a = 0 Solving 2 + -5a = 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 + -5a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5a = 0 + -2 -5a = 0 + -2 Combine like terms: 0 + -2 = -2 -5a = -2 Divide each side by '-5'. a = 0.4 Simplifying a = 0.4Solution
a = {-1, 0.4}
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