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Simplifying -3a(a + 4) + 5a + 10 = 0 Reorder the terms: -3a(4 + a) + 5a + 10 = 0 (4 * -3a + a * -3a) + 5a + 10 = 0 (-12a + -3a2) + 5a + 10 = 0 Reorder the terms: 10 + -12a + 5a + -3a2 = 0 Combine like terms: -12a + 5a = -7a 10 + -7a + -3a2 = 0 Solving 10 + -7a + -3a2 = 0 Solving for variable 'a'. Factor a trinomial. (1 + -1a)(10 + 3a) = 0Subproblem 1
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 = 1Subproblem 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 = {1, -3.333333333}
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