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Simplifying 15a2 = 13a + 20 Reorder the terms: 15a2 = 20 + 13a Solving 15a2 = 20 + 13a Solving for variable 'a'. Reorder the terms: -20 + -13a + 15a2 = 20 + 13a + -20 + -13a Reorder the terms: -20 + -13a + 15a2 = 20 + -20 + 13a + -13a Combine like terms: 20 + -20 = 0 -20 + -13a + 15a2 = 0 + 13a + -13a -20 + -13a + 15a2 = 13a + -13a Combine like terms: 13a + -13a = 0 -20 + -13a + 15a2 = 0 Factor a trinomial. (-4 + -5a)(5 + -3a) = 0Subproblem 1
Set the factor '(-4 + -5a)' equal to zero and attempt to solve: Simplifying -4 + -5a = 0 Solving -4 + -5a = 0 Move all terms containing a to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -5a = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -5a = 0 + 4 -5a = 0 + 4 Combine like terms: 0 + 4 = 4 -5a = 4 Divide each side by '-5'. a = -0.8 Simplifying a = -0.8Subproblem 2
Set the factor '(5 + -3a)' equal to zero and attempt to solve: Simplifying 5 + -3a = 0 Solving 5 + -3a = 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 + -3a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3a = 0 + -5 -3a = 0 + -5 Combine like terms: 0 + -5 = -5 -3a = -5 Divide each side by '-3'. a = 1.666666667 Simplifying a = 1.666666667Solution
a = {-0.8, 1.666666667}
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