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Simplifying 6(2a + 10) = 5a(a + 5) Reorder the terms: 6(10 + 2a) = 5a(a + 5) (10 * 6 + 2a * 6) = 5a(a + 5) (60 + 12a) = 5a(a + 5) Reorder the terms: 60 + 12a = 5a(5 + a) 60 + 12a = (5 * 5a + a * 5a) 60 + 12a = (25a + 5a2) Solving 60 + 12a = 25a + 5a2 Solving for variable 'a'. Combine like terms: 12a + -25a = -13a 60 + -13a + -5a2 = 25a + 5a2 + -25a + -5a2 Reorder the terms: 60 + -13a + -5a2 = 25a + -25a + 5a2 + -5a2 Combine like terms: 25a + -25a = 0 60 + -13a + -5a2 = 0 + 5a2 + -5a2 60 + -13a + -5a2 = 5a2 + -5a2 Combine like terms: 5a2 + -5a2 = 0 60 + -13a + -5a2 = 0 Factor a trinomial. (12 + -5a)(5 + a) = 0Subproblem 1
Set the factor '(12 + -5a)' equal to zero and attempt to solve: Simplifying 12 + -5a = 0 Solving 12 + -5a = 0 Move all terms containing a to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -5a = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -5a = 0 + -12 -5a = 0 + -12 Combine like terms: 0 + -12 = -12 -5a = -12 Divide each side by '-5'. a = 2.4 Simplifying a = 2.4Subproblem 2
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 = -5Solution
a = {2.4, -5}
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