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Simplifying (-1a + -2b) * x(a + 3b) = 0 Reorder the terms for easier multiplication: x(-1a + -2b)(a + 3b) = 0 Multiply (-1a + -2b) * (a + 3b) x(-1a * (a + 3b) + -2b * (a + 3b)) = 0 x((a * -1a + 3b * -1a) + -2b * (a + 3b)) = 0 Reorder the terms: x((-3ab + -1a2) + -2b * (a + 3b)) = 0 x((-3ab + -1a2) + -2b * (a + 3b)) = 0 x(-3ab + -1a2 + (a * -2b + 3b * -2b)) = 0 x(-3ab + -1a2 + (-2ab + -6b2)) = 0 Reorder the terms: x(-3ab + -2ab + -1a2 + -6b2) = 0 Combine like terms: -3ab + -2ab = -5ab x(-5ab + -1a2 + -6b2) = 0 (-5ab * x + -1a2 * x + -6b2 * x) = 0 (-5abx + -1a2x + -6b2x) = 0 Solving -5abx + -1a2x + -6b2x = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '-1x'. -1x(5ab + a2 + 6b2) = 0 Factor a trinomial. -1x((a + 2b)(a + 3b)) = 0 Ignore the factor -1.Subproblem 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 '(a + 2b)' equal to zero and attempt to solve: Simplifying a + 2b = 0 Solving a + 2b = 0 Move all terms containing a to the left, all other terms to the right. Add '-2b' to each side of the equation. a + 2b + -2b = 0 + -2b Combine like terms: 2b + -2b = 0 a + 0 = 0 + -2b a = 0 + -2b Remove the zero: a = -2b Simplifying a = -2bSubproblem 3
Set the factor '(a + 3b)' equal to zero and attempt to solve: Simplifying a + 3b = 0 Solving a + 3b = 0 Move all terms containing a to the left, all other terms to the right. Add '-3b' to each side of the equation. a + 3b + -3b = 0 + -3b Combine like terms: 3b + -3b = 0 a + 0 = 0 + -3b a = 0 + -3b Remove the zero: a = -3b Simplifying a = -3bSolution
a = {-2b, -3b}
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