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Simplifying 15(2a + -2) = 5(a2 + -1) Reorder the terms: 15(-2 + 2a) = 5(a2 + -1) (-2 * 15 + 2a * 15) = 5(a2 + -1) (-30 + 30a) = 5(a2 + -1) Reorder the terms: -30 + 30a = 5(-1 + a2) -30 + 30a = (-1 * 5 + a2 * 5) -30 + 30a = (-5 + 5a2) Solving -30 + 30a = -5 + 5a2 Solving for variable 'a'. Reorder the terms: -30 + 5 + 30a + -5a2 = -5 + 5a2 + 5 + -5a2 Combine like terms: -30 + 5 = -25 -25 + 30a + -5a2 = -5 + 5a2 + 5 + -5a2 Reorder the terms: -25 + 30a + -5a2 = -5 + 5 + 5a2 + -5a2 Combine like terms: -5 + 5 = 0 -25 + 30a + -5a2 = 0 + 5a2 + -5a2 -25 + 30a + -5a2 = 5a2 + -5a2 Combine like terms: 5a2 + -5a2 = 0 -25 + 30a + -5a2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-5 + 6a + -1a2) = 0 Factor a trinomial. 5((-5 + a)(1 + -1a)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-5 + a)' equal to zero and attempt to solve: Simplifying -5 + a = 0 Solving -5 + a = 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 + a = 0 + 5 Combine like terms: -5 + 5 = 0 0 + a = 0 + 5 a = 0 + 5 Combine like terms: 0 + 5 = 5 a = 5 Simplifying a = 5Subproblem 2
Set the factor '(1 + -1a)' equal to zero and attempt to solve: Simplifying 1 + -1a = 0 Solving 1 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1a = 0 + -1 -1a = 0 + -1 Combine like terms: 0 + -1 = -1 -1a = -1 Divide each side by '-1'. a = 1 Simplifying a = 1Solution
a = {5, 1}
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