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Simplifying (8a + -3x)(3a + 4x) = 0 Multiply (8a + -3x) * (3a + 4x) (8a * (3a + 4x) + -3x * (3a + 4x)) = 0 ((3a * 8a + 4x * 8a) + -3x * (3a + 4x)) = 0 Reorder the terms: ((32ax + 24a2) + -3x * (3a + 4x)) = 0 ((32ax + 24a2) + -3x * (3a + 4x)) = 0 (32ax + 24a2 + (3a * -3x + 4x * -3x)) = 0 (32ax + 24a2 + (-9ax + -12x2)) = 0 Reorder the terms: (32ax + -9ax + 24a2 + -12x2) = 0 Combine like terms: 32ax + -9ax = 23ax (23ax + 24a2 + -12x2) = 0 Solving 23ax + 24a2 + -12x2 = 0 Solving for variable 'a'. Factor a trinomial. (8a + -3x)(3a + 4x) = 0Subproblem 1
Set the factor '(8a + -3x)' equal to zero and attempt to solve: Simplifying 8a + -3x = 0 Solving 8a + -3x = 0 Move all terms containing a to the left, all other terms to the right. Add '3x' to each side of the equation. 8a + -3x + 3x = 0 + 3x Combine like terms: -3x + 3x = 0 8a + 0 = 0 + 3x 8a = 0 + 3x Remove the zero: 8a = 3x Divide each side by '8'. a = 0.375x Simplifying a = 0.375xSubproblem 2
Set the factor '(3a + 4x)' equal to zero and attempt to solve: Simplifying 3a + 4x = 0 Solving 3a + 4x = 0 Move all terms containing a to the left, all other terms to the right. Add '-4x' to each side of the equation. 3a + 4x + -4x = 0 + -4x Combine like terms: 4x + -4x = 0 3a + 0 = 0 + -4x 3a = 0 + -4x Remove the zero: 3a = -4x Divide each side by '3'. a = -1.333333333x Simplifying a = -1.333333333xSolution
a = {0.375x, -1.333333333x}
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