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Simplifying (a + -3)(a + 1) + (a + -3)(a + 4) = 0 Reorder the terms: (-3 + a)(a + 1) + (a + -3)(a + 4) = 0 Reorder the terms: (-3 + a)(1 + a) + (a + -3)(a + 4) = 0 Multiply (-3 + a) * (1 + a) (-3(1 + a) + a(1 + a)) + (a + -3)(a + 4) = 0 ((1 * -3 + a * -3) + a(1 + a)) + (a + -3)(a + 4) = 0 ((-3 + -3a) + a(1 + a)) + (a + -3)(a + 4) = 0 (-3 + -3a + (1 * a + a * a)) + (a + -3)(a + 4) = 0 (-3 + -3a + (1a + a2)) + (a + -3)(a + 4) = 0 Combine like terms: -3a + 1a = -2a (-3 + -2a + a2) + (a + -3)(a + 4) = 0 Reorder the terms: -3 + -2a + a2 + (-3 + a)(a + 4) = 0 Reorder the terms: -3 + -2a + a2 + (-3 + a)(4 + a) = 0 Multiply (-3 + a) * (4 + a) -3 + -2a + a2 + (-3(4 + a) + a(4 + a)) = 0 -3 + -2a + a2 + ((4 * -3 + a * -3) + a(4 + a)) = 0 -3 + -2a + a2 + ((-12 + -3a) + a(4 + a)) = 0 -3 + -2a + a2 + (-12 + -3a + (4 * a + a * a)) = 0 -3 + -2a + a2 + (-12 + -3a + (4a + a2)) = 0 Combine like terms: -3a + 4a = 1a -3 + -2a + a2 + (-12 + 1a + a2) = 0 Reorder the terms: -3 + -12 + -2a + 1a + a2 + a2 = 0 Combine like terms: -3 + -12 = -15 -15 + -2a + 1a + a2 + a2 = 0 Combine like terms: -2a + 1a = -1a -15 + -1a + a2 + a2 = 0 Combine like terms: a2 + a2 = 2a2 -15 + -1a + 2a2 = 0 Solving -15 + -1a + 2a2 = 0 Solving for variable 'a'. Factor a trinomial. (-5 + -2a)(3 + -1a) = 0Subproblem 1
Set the factor '(-5 + -2a)' equal to zero and attempt to solve: Simplifying -5 + -2a = 0 Solving -5 + -2a = 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 + -2a = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2a = 0 + 5 -2a = 0 + 5 Combine like terms: 0 + 5 = 5 -2a = 5 Divide each side by '-2'. a = -2.5 Simplifying a = -2.5Subproblem 2
Set the factor '(3 + -1a)' equal to zero and attempt to solve: Simplifying 3 + -1a = 0 Solving 3 + -1a = 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 + -1a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1a = 0 + -3 -1a = 0 + -3 Combine like terms: 0 + -3 = -3 -1a = -3 Divide each side by '-1'. a = 3 Simplifying a = 3Solution
a = {-2.5, 3}
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