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Simplifying a(2a + 5)(a + -2) = 0 Reorder the terms: a(5 + 2a)(a + -2) = 0 Reorder the terms: a(5 + 2a)(-2 + a) = 0 Multiply (5 + 2a) * (-2 + a) a(5(-2 + a) + 2a * (-2 + a)) = 0 a((-2 * 5 + a * 5) + 2a * (-2 + a)) = 0 a((-10 + 5a) + 2a * (-2 + a)) = 0 a(-10 + 5a + (-2 * 2a + a * 2a)) = 0 a(-10 + 5a + (-4a + 2a2)) = 0 Combine like terms: 5a + -4a = 1a a(-10 + 1a + 2a2) = 0 (-10 * a + 1a * a + 2a2 * a) = 0 (-10a + 1a2 + 2a3) = 0 Solving -10a + 1a2 + 2a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'a'. a(-10 + a + 2a2) = 0 Factor a trinomial. a((-5 + -2a)(2 + -1a)) = 0Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 2
Set the factor '(-5 + -2a)' equal to zero and attempt to solve: Simplifying -5 + -2a = 0 Solving -5 + -2a = 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 + -2a = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2a = 0 + 5 -2a = 0 + 5 Combine like terms: 0 + 5 = 5 -2a = 5 Divide each side by '-2'. a = -2.5 Simplifying a = -2.5Subproblem 3
Set the factor '(2 + -1a)' equal to zero and attempt to solve: Simplifying 2 + -1a = 0 Solving 2 + -1a = 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 + -1a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1a = 0 + -2 -1a = 0 + -2 Combine like terms: 0 + -2 = -2 -1a = -2 Divide each side by '-1'. a = 2 Simplifying a = 2Solution
a = {0, -2.5, 2}
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