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Simplifying 4(a2 + -3) = 6a + 4(a + 3) Reorder the terms: 4(-3 + a2) = 6a + 4(a + 3) (-3 * 4 + a2 * 4) = 6a + 4(a + 3) (-12 + 4a2) = 6a + 4(a + 3) Reorder the terms: -12 + 4a2 = 6a + 4(3 + a) -12 + 4a2 = 6a + (3 * 4 + a * 4) -12 + 4a2 = 6a + (12 + 4a) Reorder the terms: -12 + 4a2 = 12 + 6a + 4a Combine like terms: 6a + 4a = 10a -12 + 4a2 = 12 + 10a Solving -12 + 4a2 = 12 + 10a Solving for variable 'a'. Reorder the terms: -12 + -12 + -10a + 4a2 = 12 + 10a + -12 + -10a Combine like terms: -12 + -12 = -24 -24 + -10a + 4a2 = 12 + 10a + -12 + -10a Reorder the terms: -24 + -10a + 4a2 = 12 + -12 + 10a + -10a Combine like terms: 12 + -12 = 0 -24 + -10a + 4a2 = 0 + 10a + -10a -24 + -10a + 4a2 = 10a + -10a Combine like terms: 10a + -10a = 0 -24 + -10a + 4a2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + -5a + 2a2) = 0 Factor a trinomial. 2((-3 + -2a)(4 + -1a)) = 0 Ignore the factor 2.Subproblem 1
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 = -1.5Subproblem 2
Set the factor '(4 + -1a)' equal to zero and attempt to solve: Simplifying 4 + -1a = 0 Solving 4 + -1a = 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 + -1a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1a = 0 + -4 -1a = 0 + -4 Combine like terms: 0 + -4 = -4 -1a = -4 Divide each side by '-1'. a = 4 Simplifying a = 4Solution
a = {-1.5, 4}
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