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Simplifying 10(a + -6) + -3a(a + -6) = 0 Reorder the terms: 10(-6 + a) + -3a(a + -6) = 0 (-6 * 10 + a * 10) + -3a(a + -6) = 0 (-60 + 10a) + -3a(a + -6) = 0 Reorder the terms: -60 + 10a + -3a(-6 + a) = 0 -60 + 10a + (-6 * -3a + a * -3a) = 0 -60 + 10a + (18a + -3a2) = 0 Combine like terms: 10a + 18a = 28a -60 + 28a + -3a2 = 0 Solving -60 + 28a + -3a2 = 0 Solving for variable 'a'. Factor a trinomial. (-6 + a)(10 + -3a) = 0Subproblem 1
Set the factor '(-6 + a)' equal to zero and attempt to solve: Simplifying -6 + a = 0 Solving -6 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + a = 0 + 6 Combine like terms: -6 + 6 = 0 0 + a = 0 + 6 a = 0 + 6 Combine like terms: 0 + 6 = 6 a = 6 Simplifying a = 6Subproblem 2
Set the factor '(10 + -3a)' equal to zero and attempt to solve: Simplifying 10 + -3a = 0 Solving 10 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -3a = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -3a = 0 + -10 -3a = 0 + -10 Combine like terms: 0 + -10 = -10 -3a = -10 Divide each side by '-3'. a = 3.333333333 Simplifying a = 3.333333333Solution
a = {6, 3.333333333}
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