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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 = -17a (35 + -17a + 2a2) = 0 Solving 35 + -17a + 2a2 = 0 Solving for variable 'a'. Factor a trinomial. (7 + -2a)(5 + -1a) = 0Subproblem 1
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 = 3.5Subproblem 2
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 = 5Solution
a = {3.5, 5}
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