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Simplifying (x + 2a)(x + 3a) = 0 Reorder the terms: (2a + x)(x + 3a) = 0 Reorder the terms: (2a + x)(3a + x) = 0 Multiply (2a + x) * (3a + x) (2a * (3a + x) + x(3a + x)) = 0 ((3a * 2a + x * 2a) + x(3a + x)) = 0 Reorder the terms: ((2ax + 6a2) + x(3a + x)) = 0 ((2ax + 6a2) + x(3a + x)) = 0 (2ax + 6a2 + (3a * x + x * x)) = 0 (2ax + 6a2 + (3ax + x2)) = 0 Reorder the terms: (2ax + 3ax + 6a2 + x2) = 0 Combine like terms: 2ax + 3ax = 5ax (5ax + 6a2 + x2) = 0 Solving 5ax + 6a2 + x2 = 0 Solving for variable 'a'. Factor a trinomial. (3a + x)(2a + x) = 0Subproblem 1
Set the factor '(3a + x)' equal to zero and attempt to solve: Simplifying 3a + x = 0 Solving 3a + x = 0 Move all terms containing a to the left, all other terms to the right. Add '-1x' to each side of the equation. 3a + x + -1x = 0 + -1x Combine like terms: x + -1x = 0 3a + 0 = 0 + -1x 3a = 0 + -1x Remove the zero: 3a = -1x Divide each side by '3'. a = -0.3333333333x Simplifying a = -0.3333333333xSubproblem 2
Set the factor '(2a + x)' equal to zero and attempt to solve: Simplifying 2a + x = 0 Solving 2a + x = 0 Move all terms containing a to the left, all other terms to the right. Add '-1x' to each side of the equation. 2a + x + -1x = 0 + -1x Combine like terms: x + -1x = 0 2a + 0 = 0 + -1x 2a = 0 + -1x Remove the zero: 2a = -1x Divide each side by '2'. a = -0.5x Simplifying a = -0.5xSolution
a = {-0.3333333333x, -0.5x}
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