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Simplifying (3a + -2) * x(a + 3) = 0 Reorder the terms: (-2 + 3a) * x(a + 3) = 0 Reorder the terms: (-2 + 3a) * x(3 + a) = 0 Reorder the terms for easier multiplication: x(-2 + 3a)(3 + a) = 0 Multiply (-2 + 3a) * (3 + a) x(-2(3 + a) + 3a * (3 + a)) = 0 x((3 * -2 + a * -2) + 3a * (3 + a)) = 0 x((-6 + -2a) + 3a * (3 + a)) = 0 x(-6 + -2a + (3 * 3a + a * 3a)) = 0 x(-6 + -2a + (9a + 3a2)) = 0 Combine like terms: -2a + 9a = 7a x(-6 + 7a + 3a2) = 0 (-6 * x + 7a * x + 3a2 * x) = 0 Reorder the terms: (7ax + 3a2x + -6x) = 0 (7ax + 3a2x + -6x) = 0 Solving 7ax + 3a2x + -6x = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'x'. x(7a + 3a2 + -6) = 0 Factor a trinomial. x((3a + -2)(a + 3)) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing a to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x = 0 + -1x Remove the zero: 0 = -1x Simplifying 0 = -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(3a + -2)' equal to zero and attempt to solve: Simplifying 3a + -2 = 0 Reorder the terms: -2 + 3a = 0 Solving -2 + 3a = 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 + 3a = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 3a = 0 + 2 3a = 0 + 2 Combine like terms: 0 + 2 = 2 3a = 2 Divide each side by '3'. a = 0.6666666667 Simplifying a = 0.6666666667Subproblem 3
Set the factor '(a + 3)' equal to zero and attempt to solve: Simplifying a + 3 = 0 Reorder the terms: 3 + a = 0 Solving 3 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + a = 0 + -3 a = 0 + -3 Combine like terms: 0 + -3 = -3 a = -3 Simplifying a = -3Solution
a = {0.6666666667, -3}
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