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Simplifying (5a + -2)(2a + -3) = 0 Reorder the terms: (-2 + 5a)(2a + -3) = 0 Reorder the terms: (-2 + 5a)(-3 + 2a) = 0 Multiply (-2 + 5a) * (-3 + 2a) (-2(-3 + 2a) + 5a * (-3 + 2a)) = 0 ((-3 * -2 + 2a * -2) + 5a * (-3 + 2a)) = 0 ((6 + -4a) + 5a * (-3 + 2a)) = 0 (6 + -4a + (-3 * 5a + 2a * 5a)) = 0 (6 + -4a + (-15a + 10a2)) = 0 Combine like terms: -4a + -15a = -19a (6 + -19a + 10a2) = 0 Solving 6 + -19a + 10a2 = 0 Solving for variable 'a'. Factor a trinomial. (2 + -5a)(3 + -2a) = 0Subproblem 1
Set the factor '(2 + -5a)' equal to zero and attempt to solve: Simplifying 2 + -5a = 0 Solving 2 + -5a = 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 + -5a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5a = 0 + -2 -5a = 0 + -2 Combine like terms: 0 + -2 = -2 -5a = -2 Divide each side by '-5'. a = 0.4 Simplifying a = 0.4Subproblem 2
Set the factor '(3 + -2a)' equal to zero and attempt to solve: Simplifying 3 + -2a = 0 Solving 3 + -2a = 0 Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2a = 0 + -3 -2a = 0 + -3 Combine like terms: 0 + -3 = -3 -2a = -3 Divide each side by '-2'. a = 1.5 Simplifying a = 1.5Solution
a = {0.4, 1.5}
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