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Simplifying 0 = x3 + 4x2 + 3x Reorder the terms: 0 = 3x + 4x2 + x3 Solving 0 = 3x + 4x2 + x3 Solving for variable 'x'. Remove the zero: -3x + -4x2 + -1x3 = 3x + 4x2 + x3 + -3x + -4x2 + -1x3 Reorder the terms: -3x + -4x2 + -1x3 = 3x + -3x + 4x2 + -4x2 + x3 + -1x3 Combine like terms: 3x + -3x = 0 -3x + -4x2 + -1x3 = 0 + 4x2 + -4x2 + x3 + -1x3 -3x + -4x2 + -1x3 = 4x2 + -4x2 + x3 + -1x3 Combine like terms: 4x2 + -4x2 = 0 -3x + -4x2 + -1x3 = 0 + x3 + -1x3 -3x + -4x2 + -1x3 = x3 + -1x3 Combine like terms: x3 + -1x3 = 0 -3x + -4x2 + -1x3 = 0 Factor out the Greatest Common Factor (GCF), '-1x'. -1x(3 + 4x + x2) = 0 Factor a trinomial. -1x((3 + x)(1 + x)) = 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 x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Subproblem 3
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Solution
x = {0, -3, -1}
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