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Simplifying (4a + -7)(8a + 3) = 0 Reorder the terms: (-7 + 4a)(8a + 3) = 0 Reorder the terms: (-7 + 4a)(3 + 8a) = 0 Multiply (-7 + 4a) * (3 + 8a) (-7(3 + 8a) + 4a * (3 + 8a)) = 0 ((3 * -7 + 8a * -7) + 4a * (3 + 8a)) = 0 ((-21 + -56a) + 4a * (3 + 8a)) = 0 (-21 + -56a + (3 * 4a + 8a * 4a)) = 0 (-21 + -56a + (12a + 32a2)) = 0 Combine like terms: -56a + 12a = -44a (-21 + -44a + 32a2) = 0 Solving -21 + -44a + 32a2 = 0 Solving for variable 'a'. Factor a trinomial. (-3 + -8a)(7 + -4a) = 0Subproblem 1
Set the factor '(-3 + -8a)' equal to zero and attempt to solve: Simplifying -3 + -8a = 0 Solving -3 + -8a = 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 + -8a = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -8a = 0 + 3 -8a = 0 + 3 Combine like terms: 0 + 3 = 3 -8a = 3 Divide each side by '-8'. a = -0.375 Simplifying a = -0.375Subproblem 2
Set the factor '(7 + -4a)' equal to zero and attempt to solve: Simplifying 7 + -4a = 0 Solving 7 + -4a = 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 + -4a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4a = 0 + -7 -4a = 0 + -7 Combine like terms: 0 + -7 = -7 -4a = -7 Divide each side by '-4'. a = 1.75 Simplifying a = 1.75Solution
a = {-0.375, 1.75}
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