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Simplifying 2x * x(x + 3) + -1x(x + 1)(x + 3) = 0 Reorder the terms: 2x * x(3 + x) + -1x(x + 1)(x + 3) = 0 Multiply x * x 2x2(3 + x) + -1x(x + 1)(x + 3) = 0 (3 * 2x2 + x * 2x2) + -1x(x + 1)(x + 3) = 0 (6x2 + 2x3) + -1x(x + 1)(x + 3) = 0 Reorder the terms: 6x2 + 2x3 + -1x(1 + x)(x + 3) = 0 Reorder the terms: 6x2 + 2x3 + -1x(1 + x)(3 + x) = 0 Multiply (1 + x) * (3 + x) 6x2 + 2x3 + -1x(1(3 + x) + x(3 + x)) = 0 6x2 + 2x3 + -1x((3 * 1 + x * 1) + x(3 + x)) = 0 6x2 + 2x3 + -1x((3 + 1x) + x(3 + x)) = 0 6x2 + 2x3 + -1x(3 + 1x + (3 * x + x * x)) = 0 6x2 + 2x3 + -1x(3 + 1x + (3x + x2)) = 0 Combine like terms: 1x + 3x = 4x 6x2 + 2x3 + -1x(3 + 4x + x2) = 0 6x2 + 2x3 + (3 * -1x + 4x * -1x + x2 * -1x) = 0 6x2 + 2x3 + (-3x + -4x2 + -1x3) = 0 Reorder the terms: -3x + 6x2 + -4x2 + 2x3 + -1x3 = 0 Combine like terms: 6x2 + -4x2 = 2x2 -3x + 2x2 + 2x3 + -1x3 = 0 Combine like terms: 2x3 + -1x3 = 1x3 -3x + 2x2 + 1x3 = 0 Solving -3x + 2x2 + 1x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-3 + 2x + x2) = 0 Factor a trinomial. x((-3 + -1x)(1 + -1x)) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-3 + -1x)' equal to zero and attempt to solve: Simplifying -3 + -1x = 0 Solving -3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x = 0 + 3 -1x = 0 + 3 Combine like terms: 0 + 3 = 3 -1x = 3 Divide each side by '-1'. x = -3 Simplifying x = -3Subproblem 3
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {0, -3, 1}
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