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Simplifying (a + -4)(a + 7) + (a + -4)(a + 8) = 0 Reorder the terms: (-4 + a)(a + 7) + (a + -4)(a + 8) = 0 Reorder the terms: (-4 + a)(7 + a) + (a + -4)(a + 8) = 0 Multiply (-4 + a) * (7 + a) (-4(7 + a) + a(7 + a)) + (a + -4)(a + 8) = 0 ((7 * -4 + a * -4) + a(7 + a)) + (a + -4)(a + 8) = 0 ((-28 + -4a) + a(7 + a)) + (a + -4)(a + 8) = 0 (-28 + -4a + (7 * a + a * a)) + (a + -4)(a + 8) = 0 (-28 + -4a + (7a + a2)) + (a + -4)(a + 8) = 0 Combine like terms: -4a + 7a = 3a (-28 + 3a + a2) + (a + -4)(a + 8) = 0 Reorder the terms: -28 + 3a + a2 + (-4 + a)(a + 8) = 0 Reorder the terms: -28 + 3a + a2 + (-4 + a)(8 + a) = 0 Multiply (-4 + a) * (8 + a) -28 + 3a + a2 + (-4(8 + a) + a(8 + a)) = 0 -28 + 3a + a2 + ((8 * -4 + a * -4) + a(8 + a)) = 0 -28 + 3a + a2 + ((-32 + -4a) + a(8 + a)) = 0 -28 + 3a + a2 + (-32 + -4a + (8 * a + a * a)) = 0 -28 + 3a + a2 + (-32 + -4a + (8a + a2)) = 0 Combine like terms: -4a + 8a = 4a -28 + 3a + a2 + (-32 + 4a + a2) = 0 Reorder the terms: -28 + -32 + 3a + 4a + a2 + a2 = 0 Combine like terms: -28 + -32 = -60 -60 + 3a + 4a + a2 + a2 = 0 Combine like terms: 3a + 4a = 7a -60 + 7a + a2 + a2 = 0 Combine like terms: a2 + a2 = 2a2 -60 + 7a + 2a2 = 0 Solving -60 + 7a + 2a2 = 0 Solving for variable 'a'. Factor a trinomial. (-15 + -2a)(4 + -1a) = 0Subproblem 1
Set the factor '(-15 + -2a)' equal to zero and attempt to solve: Simplifying -15 + -2a = 0 Solving -15 + -2a = 0 Move all terms containing a to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + -2a = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -2a = 0 + 15 -2a = 0 + 15 Combine like terms: 0 + 15 = 15 -2a = 15 Divide each side by '-2'. a = -7.5 Simplifying a = -7.5Subproblem 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 = {-7.5, 4}
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