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Simplifying (a + 5)(2a + -7) = 0 Reorder the terms: (5 + a)(2a + -7) = 0 Reorder the terms: (5 + a)(-7 + 2a) = 0 Multiply (5 + a) * (-7 + 2a) (5(-7 + 2a) + a(-7 + 2a)) = 0 ((-7 * 5 + 2a * 5) + a(-7 + 2a)) = 0 ((-35 + 10a) + a(-7 + 2a)) = 0 (-35 + 10a + (-7 * a + 2a * a)) = 0 (-35 + 10a + (-7a + 2a2)) = 0 Combine like terms: 10a + -7a = 3a (-35 + 3a + 2a2) = 0 Solving -35 + 3a + 2a2 = 0 Solving for variable 'a'. Factor a trinomial. (-5 + -1a)(7 + -2a) = 0Subproblem 1
Set the factor '(-5 + -1a)' equal to zero and attempt to solve: Simplifying -5 + -1a = 0 Solving -5 + -1a = 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 + -1a = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1a = 0 + 5 -1a = 0 + 5 Combine like terms: 0 + 5 = 5 -1a = 5 Divide each side by '-1'. a = -5 Simplifying a = -5Subproblem 2
Set the factor '(7 + -2a)' equal to zero and attempt to solve: Simplifying 7 + -2a = 0 Solving 7 + -2a = 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 + -2a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2a = 0 + -7 -2a = 0 + -7 Combine like terms: 0 + -7 = -7 -2a = -7 Divide each side by '-2'. a = 3.5 Simplifying a = 3.5Solution
a = {-5, 3.5}
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