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Simplifying 5(a + -3) + -2a(a + -3) = 0 Reorder the terms: 5(-3 + a) + -2a(a + -3) = 0 (-3 * 5 + a * 5) + -2a(a + -3) = 0 (-15 + 5a) + -2a(a + -3) = 0 Reorder the terms: -15 + 5a + -2a(-3 + a) = 0 -15 + 5a + (-3 * -2a + a * -2a) = 0 -15 + 5a + (6a + -2a2) = 0 Combine like terms: 5a + 6a = 11a -15 + 11a + -2a2 = 0 Solving -15 + 11a + -2a2 = 0 Solving for variable 'a'. Factor a trinomial. (-3 + a)(5 + -2a) = 0Subproblem 1
Set the factor '(-3 + a)' equal to zero and attempt to solve: Simplifying -3 + a = 0 Solving -3 + a = 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 + a = 0 + 3 Combine like terms: -3 + 3 = 0 0 + a = 0 + 3 a = 0 + 3 Combine like terms: 0 + 3 = 3 a = 3 Simplifying a = 3Subproblem 2
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 = 2.5Solution
a = {3, 2.5}
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