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Simplifying (5a + 1)(a + -2) = 0 Reorder the terms: (1 + 5a)(a + -2) = 0 Reorder the terms: (1 + 5a)(-2 + a) = 0 Multiply (1 + 5a) * (-2 + a) (1(-2 + a) + 5a * (-2 + a)) = 0 ((-2 * 1 + a * 1) + 5a * (-2 + a)) = 0 ((-2 + 1a) + 5a * (-2 + a)) = 0 (-2 + 1a + (-2 * 5a + a * 5a)) = 0 (-2 + 1a + (-10a + 5a2)) = 0 Combine like terms: 1a + -10a = -9a (-2 + -9a + 5a2) = 0 Solving -2 + -9a + 5a2 = 0 Solving for variable 'a'. Factor a trinomial. (-1 + -5a)(2 + -1a) = 0Subproblem 1
Set the factor '(-1 + -5a)' equal to zero and attempt to solve: Simplifying -1 + -5a = 0 Solving -1 + -5a = 0 Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -5a = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -5a = 0 + 1 -5a = 0 + 1 Combine like terms: 0 + 1 = 1 -5a = 1 Divide each side by '-5'. a = -0.2 Simplifying a = -0.2Subproblem 2
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, 2}
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