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Simplifying (13a + 9)(4a + -7) = 0 Reorder the terms: (9 + 13a)(4a + -7) = 0 Reorder the terms: (9 + 13a)(-7 + 4a) = 0 Multiply (9 + 13a) * (-7 + 4a) (9(-7 + 4a) + 13a * (-7 + 4a)) = 0 ((-7 * 9 + 4a * 9) + 13a * (-7 + 4a)) = 0 ((-63 + 36a) + 13a * (-7 + 4a)) = 0 (-63 + 36a + (-7 * 13a + 4a * 13a)) = 0 (-63 + 36a + (-91a + 52a2)) = 0 Combine like terms: 36a + -91a = -55a (-63 + -55a + 52a2) = 0 Solving -63 + -55a + 52a2 = 0 Solving for variable 'a'. Factor a trinomial. (-9 + -13a)(7 + -4a) = 0Subproblem 1
Set the factor '(-9 + -13a)' equal to zero and attempt to solve: Simplifying -9 + -13a = 0 Solving -9 + -13a = 0 Move all terms containing a to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -13a = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -13a = 0 + 9 -13a = 0 + 9 Combine like terms: 0 + 9 = 9 -13a = 9 Divide each side by '-13'. a = -0.6923076923 Simplifying a = -0.6923076923Subproblem 2
Set the factor '(7 + -4a)' equal to zero and attempt to solve: Simplifying 7 + -4a = 0 Solving 7 + -4a = 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 + -4a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4a = 0 + -7 -4a = 0 + -7 Combine like terms: 0 + -7 = -7 -4a = -7 Divide each side by '-4'. a = 1.75 Simplifying a = 1.75Solution
a = {-0.6923076923, 1.75}
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