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Simplifying (3a + -4)(4a + -3) = 0 Reorder the terms: (-4 + 3a)(4a + -3) = 0 Reorder the terms: (-4 + 3a)(-3 + 4a) = 0 Multiply (-4 + 3a) * (-3 + 4a) (-4(-3 + 4a) + 3a * (-3 + 4a)) = 0 ((-3 * -4 + 4a * -4) + 3a * (-3 + 4a)) = 0 ((12 + -16a) + 3a * (-3 + 4a)) = 0 (12 + -16a + (-3 * 3a + 4a * 3a)) = 0 (12 + -16a + (-9a + 12a2)) = 0 Combine like terms: -16a + -9a = -25a (12 + -25a + 12a2) = 0 Solving 12 + -25a + 12a2 = 0 Solving for variable 'a'. Factor a trinomial. (3 + -4a)(4 + -3a) = 0Subproblem 1
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 = 0.75Subproblem 2
Set the factor '(4 + -3a)' equal to zero and attempt to solve: Simplifying 4 + -3a = 0 Solving 4 + -3a = 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 + -3a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3a = 0 + -4 -3a = 0 + -4 Combine like terms: 0 + -4 = -4 -3a = -4 Divide each side by '-3'. a = 1.333333333 Simplifying a = 1.333333333Solution
a = {0.75, 1.333333333}
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