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Simplifying (7a + 4)(3a + -5) = 0 Reorder the terms: (4 + 7a)(3a + -5) = 0 Reorder the terms: (4 + 7a)(-5 + 3a) = 0 Multiply (4 + 7a) * (-5 + 3a) (4(-5 + 3a) + 7a * (-5 + 3a)) = 0 ((-5 * 4 + 3a * 4) + 7a * (-5 + 3a)) = 0 ((-20 + 12a) + 7a * (-5 + 3a)) = 0 (-20 + 12a + (-5 * 7a + 3a * 7a)) = 0 (-20 + 12a + (-35a + 21a2)) = 0 Combine like terms: 12a + -35a = -23a (-20 + -23a + 21a2) = 0 Solving -20 + -23a + 21a2 = 0 Solving for variable 'a'. Factor a trinomial. (-4 + -7a)(5 + -3a) = 0Subproblem 1
Set the factor '(-4 + -7a)' equal to zero and attempt to solve: Simplifying -4 + -7a = 0 Solving -4 + -7a = 0 Move all terms containing a to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -7a = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -7a = 0 + 4 -7a = 0 + 4 Combine like terms: 0 + 4 = 4 -7a = 4 Divide each side by '-7'. a = -0.5714285714 Simplifying a = -0.5714285714Subproblem 2
Set the factor '(5 + -3a)' equal to zero and attempt to solve: Simplifying 5 + -3a = 0 Solving 5 + -3a = 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 + -3a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3a = 0 + -5 -3a = 0 + -5 Combine like terms: 0 + -5 = -5 -3a = -5 Divide each side by '-3'. a = 1.666666667 Simplifying a = 1.666666667Solution
a = {-0.5714285714, 1.666666667}
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