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Simplifying (4a + 5)(3a + -7) = 0 Reorder the terms: (5 + 4a)(3a + -7) = 0 Reorder the terms: (5 + 4a)(-7 + 3a) = 0 Multiply (5 + 4a) * (-7 + 3a) (5(-7 + 3a) + 4a * (-7 + 3a)) = 0 ((-7 * 5 + 3a * 5) + 4a * (-7 + 3a)) = 0 ((-35 + 15a) + 4a * (-7 + 3a)) = 0 (-35 + 15a + (-7 * 4a + 3a * 4a)) = 0 (-35 + 15a + (-28a + 12a2)) = 0 Combine like terms: 15a + -28a = -13a (-35 + -13a + 12a2) = 0 Solving -35 + -13a + 12a2 = 0 Solving for variable 'a'. Factor a trinomial. (-5 + -4a)(7 + -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 '(7 + -3a)' equal to zero and attempt to solve: Simplifying 7 + -3a = 0 Solving 7 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -3a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3a = 0 + -7 -3a = 0 + -7 Combine like terms: 0 + -7 = -7 -3a = -7 Divide each side by '-3'. a = 2.333333333 Simplifying a = 2.333333333Solution
a = {-1.25, 2.333333333}
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