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Simplifying (3a + -2)(4a + 5) = 0 Reorder the terms: (-2 + 3a)(4a + 5) = 0 Reorder the terms: (-2 + 3a)(5 + 4a) = 0 Multiply (-2 + 3a) * (5 + 4a) (-2(5 + 4a) + 3a * (5 + 4a)) = 0 ((5 * -2 + 4a * -2) + 3a * (5 + 4a)) = 0 ((-10 + -8a) + 3a * (5 + 4a)) = 0 (-10 + -8a + (5 * 3a + 4a * 3a)) = 0 (-10 + -8a + (15a + 12a2)) = 0 Combine like terms: -8a + 15a = 7a (-10 + 7a + 12a2) = 0 Solving -10 + 7a + 12a2 = 0 Solving for variable 'a'. Factor a trinomial. (-5 + -4a)(2 + -3a) = 0Subproblem 1
Set the factor '(-5 + -4a)' equal to zero and attempt to solve: Simplifying -5 + -4a = 0 Solving -5 + -4a = 0 Move all terms containing a to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -4a = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -4a = 0 + 5 -4a = 0 + 5 Combine like terms: 0 + 5 = 5 -4a = 5 Divide each side by '-4'. a = -1.25 Simplifying a = -1.25Subproblem 2
Set the factor '(2 + -3a)' equal to zero and attempt to solve: Simplifying 2 + -3a = 0 Solving 2 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3a = 0 + -2 -3a = 0 + -2 Combine like terms: 0 + -2 = -2 -3a = -2 Divide each side by '-3'. a = 0.6666666667 Simplifying a = 0.6666666667Solution
a = {-1.25, 0.6666666667}
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