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Simplifying 12a2 + 9a = 16a + 12 Reorder the terms: 9a + 12a2 = 16a + 12 Reorder the terms: 9a + 12a2 = 12 + 16a Solving 9a + 12a2 = 12 + 16a Solving for variable 'a'. Reorder the terms: -12 + 9a + -16a + 12a2 = 12 + 16a + -12 + -16a Combine like terms: 9a + -16a = -7a -12 + -7a + 12a2 = 12 + 16a + -12 + -16a Reorder the terms: -12 + -7a + 12a2 = 12 + -12 + 16a + -16a Combine like terms: 12 + -12 = 0 -12 + -7a + 12a2 = 0 + 16a + -16a -12 + -7a + 12a2 = 16a + -16a Combine like terms: 16a + -16a = 0 -12 + -7a + 12a2 = 0 Factor a trinomial. (-3 + -4a)(4 + -3a) = 0Subproblem 1
Set the factor '(-3 + -4a)' equal to zero and attempt to solve: Simplifying -3 + -4a = 0 Solving -3 + -4a = 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 + -4a = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4a = 0 + 3 -4a = 0 + 3 Combine like terms: 0 + 3 = 3 -4a = 3 Divide each side by '-4'. a = -0.75 Simplifying a = -0.75Subproblem 2
Set the factor '(4 + -3a)' equal to zero and attempt to solve: Simplifying 4 + -3a = 0 Solving 4 + -3a = 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 + -3a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3a = 0 + -4 -3a = 0 + -4 Combine like terms: 0 + -4 = -4 -3a = -4 Divide each side by '-3'. a = 1.333333333 Simplifying a = 1.333333333Solution
a = {-0.75, 1.333333333}
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