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Simplifying (a + 3)(a + 4) = -10(a + -5) Reorder the terms: (3 + a)(a + 4) = -10(a + -5) Reorder the terms: (3 + a)(4 + a) = -10(a + -5) Multiply (3 + a) * (4 + a) (3(4 + a) + a(4 + a)) = -10(a + -5) ((4 * 3 + a * 3) + a(4 + a)) = -10(a + -5) ((12 + 3a) + a(4 + a)) = -10(a + -5) (12 + 3a + (4 * a + a * a)) = -10(a + -5) (12 + 3a + (4a + a2)) = -10(a + -5) Combine like terms: 3a + 4a = 7a (12 + 7a + a2) = -10(a + -5) Reorder the terms: 12 + 7a + a2 = -10(-5 + a) 12 + 7a + a2 = (-5 * -10 + a * -10) 12 + 7a + a2 = (50 + -10a) Solving 12 + 7a + a2 = 50 + -10a Solving for variable 'a'. Reorder the terms: 12 + -50 + 7a + 10a + a2 = 50 + -10a + -50 + 10a Combine like terms: 12 + -50 = -38 -38 + 7a + 10a + a2 = 50 + -10a + -50 + 10a Combine like terms: 7a + 10a = 17a -38 + 17a + a2 = 50 + -10a + -50 + 10a Reorder the terms: -38 + 17a + a2 = 50 + -50 + -10a + 10a Combine like terms: 50 + -50 = 0 -38 + 17a + a2 = 0 + -10a + 10a -38 + 17a + a2 = -10a + 10a Combine like terms: -10a + 10a = 0 -38 + 17a + a2 = 0 Factor a trinomial. (-19 + -1a)(2 + -1a) = 0Subproblem 1
Set the factor '(-19 + -1a)' equal to zero and attempt to solve: Simplifying -19 + -1a = 0 Solving -19 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + -1a = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -1a = 0 + 19 -1a = 0 + 19 Combine like terms: 0 + 19 = 19 -1a = 19 Divide each side by '-1'. a = -19 Simplifying a = -19Subproblem 2
Set the factor '(2 + -1a)' equal to zero and attempt to solve: Simplifying 2 + -1a = 0 Solving 2 + -1a = 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 + -1a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1a = 0 + -2 -1a = 0 + -2 Combine like terms: 0 + -2 = -2 -1a = -2 Divide each side by '-1'. a = 2 Simplifying a = 2Solution
a = {-19, 2}
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