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Simplifying (4a + 3)(5a + -3) = 0 Reorder the terms: (3 + 4a)(5a + -3) = 0 Reorder the terms: (3 + 4a)(-3 + 5a) = 0 Multiply (3 + 4a) * (-3 + 5a) (3(-3 + 5a) + 4a * (-3 + 5a)) = 0 ((-3 * 3 + 5a * 3) + 4a * (-3 + 5a)) = 0 ((-9 + 15a) + 4a * (-3 + 5a)) = 0 (-9 + 15a + (-3 * 4a + 5a * 4a)) = 0 (-9 + 15a + (-12a + 20a2)) = 0 Combine like terms: 15a + -12a = 3a (-9 + 3a + 20a2) = 0 Solving -9 + 3a + 20a2 = 0 Solving for variable 'a'. Factor a trinomial. (-3 + -4a)(3 + -5a) = 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 '(3 + -5a)' equal to zero and attempt to solve: Simplifying 3 + -5a = 0 Solving 3 + -5a = 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 + -5a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5a = 0 + -3 -5a = 0 + -3 Combine like terms: 0 + -3 = -3 -5a = -3 Divide each side by '-5'. a = 0.6 Simplifying a = 0.6Solution
a = {-0.75, 0.6}
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