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Simplifying 5a(a + -3) + -7(a + -3) = 0 Reorder the terms: 5a(-3 + a) + -7(a + -3) = 0 (-3 * 5a + a * 5a) + -7(a + -3) = 0 (-15a + 5a2) + -7(a + -3) = 0 Reorder the terms: -15a + 5a2 + -7(-3 + a) = 0 -15a + 5a2 + (-3 * -7 + a * -7) = 0 -15a + 5a2 + (21 + -7a) = 0 Reorder the terms: 21 + -15a + -7a + 5a2 = 0 Combine like terms: -15a + -7a = -22a 21 + -22a + 5a2 = 0 Solving 21 + -22a + 5a2 = 0 Solving for variable 'a'. Factor a trinomial. (7 + -5a)(3 + -1a) = 0Subproblem 1
Set the factor '(7 + -5a)' equal to zero and attempt to solve: Simplifying 7 + -5a = 0 Solving 7 + -5a = 0 Move all terms containing a to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -5a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5a = 0 + -7 -5a = 0 + -7 Combine like terms: 0 + -7 = -7 -5a = -7 Divide each side by '-5'. a = 1.4 Simplifying a = 1.4Subproblem 2
Set the factor '(3 + -1a)' equal to zero and attempt to solve: Simplifying 3 + -1a = 0 Solving 3 + -1a = 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 + -1a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1a = 0 + -3 -1a = 0 + -3 Combine like terms: 0 + -3 = -3 -1a = -3 Divide each side by '-1'. a = 3 Simplifying a = 3Solution
a = {1.4, 3}
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