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Simplifying (4a + -3)(8a + 7) = 0 Reorder the terms: (-3 + 4a)(8a + 7) = 0 Reorder the terms: (-3 + 4a)(7 + 8a) = 0 Multiply (-3 + 4a) * (7 + 8a) (-3(7 + 8a) + 4a * (7 + 8a)) = 0 ((7 * -3 + 8a * -3) + 4a * (7 + 8a)) = 0 ((-21 + -24a) + 4a * (7 + 8a)) = 0 (-21 + -24a + (7 * 4a + 8a * 4a)) = 0 (-21 + -24a + (28a + 32a2)) = 0 Combine like terms: -24a + 28a = 4a (-21 + 4a + 32a2) = 0 Solving -21 + 4a + 32a2 = 0 Solving for variable 'a'. Factor a trinomial. (-7 + -8a)(3 + -4a) = 0Subproblem 1
Set the factor '(-7 + -8a)' equal to zero and attempt to solve: Simplifying -7 + -8a = 0 Solving -7 + -8a = 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 + -8a = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -8a = 0 + 7 -8a = 0 + 7 Combine like terms: 0 + 7 = 7 -8a = 7 Divide each side by '-8'. a = -0.875 Simplifying a = -0.875Subproblem 2
Set the factor '(3 + -4a)' equal to zero and attempt to solve: Simplifying 3 + -4a = 0 Solving 3 + -4a = 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 + -4a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4a = 0 + -3 -4a = 0 + -3 Combine like terms: 0 + -3 = -3 -4a = -3 Divide each side by '-4'. a = 0.75 Simplifying a = 0.75Solution
a = {-0.875, 0.75}
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