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Simplifying (8a + -4)(8a + 3) = 0 Reorder the terms: (-4 + 8a)(8a + 3) = 0 Reorder the terms: (-4 + 8a)(3 + 8a) = 0 Multiply (-4 + 8a) * (3 + 8a) (-4(3 + 8a) + 8a * (3 + 8a)) = 0 ((3 * -4 + 8a * -4) + 8a * (3 + 8a)) = 0 ((-12 + -32a) + 8a * (3 + 8a)) = 0 (-12 + -32a + (3 * 8a + 8a * 8a)) = 0 (-12 + -32a + (24a + 64a2)) = 0 Combine like terms: -32a + 24a = -8a (-12 + -8a + 64a2) = 0 Solving -12 + -8a + 64a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '4'. 4(-3 + -2a + 16a2) = 0 Factor a trinomial. 4((-3 + -8a)(1 + -2a)) = 0 Ignore the factor 4.Subproblem 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 '(1 + -2a)' equal to zero and attempt to solve: Simplifying 1 + -2a = 0 Solving 1 + -2a = 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 + -2a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2a = 0 + -1 -2a = 0 + -1 Combine like terms: 0 + -1 = -1 -2a = -1 Divide each side by '-2'. a = 0.5 Simplifying a = 0.5Solution
a = {-0.375, 0.5}
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