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Simplifying (10a + 2)(2a + -4) = 0 Reorder the terms: (2 + 10a)(2a + -4) = 0 Reorder the terms: (2 + 10a)(-4 + 2a) = 0 Multiply (2 + 10a) * (-4 + 2a) (2(-4 + 2a) + 10a * (-4 + 2a)) = 0 ((-4 * 2 + 2a * 2) + 10a * (-4 + 2a)) = 0 ((-8 + 4a) + 10a * (-4 + 2a)) = 0 (-8 + 4a + (-4 * 10a + 2a * 10a)) = 0 (-8 + 4a + (-40a + 20a2)) = 0 Combine like terms: 4a + -40a = -36a (-8 + -36a + 20a2) = 0 Solving -8 + -36a + 20a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '4'. 4(-2 + -9a + 5a2) = 0 Factor a trinomial. 4((-1 + -5a)(2 + -1a)) = 0 Ignore the factor 4.Subproblem 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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