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Simplifying 0 = x4 + 3x3 + -4x2 Reorder the terms: 0 = -4x2 + 3x3 + x4 Solving 0 = -4x2 + 3x3 + x4 Solving for variable 'x'. Remove the zero: 4x2 + -3x3 + -1x4 = -4x2 + 3x3 + x4 + 4x2 + -3x3 + -1x4 Reorder the terms: 4x2 + -3x3 + -1x4 = -4x2 + 4x2 + 3x3 + -3x3 + x4 + -1x4 Combine like terms: -4x2 + 4x2 = 0 4x2 + -3x3 + -1x4 = 0 + 3x3 + -3x3 + x4 + -1x4 4x2 + -3x3 + -1x4 = 3x3 + -3x3 + x4 + -1x4 Combine like terms: 3x3 + -3x3 = 0 4x2 + -3x3 + -1x4 = 0 + x4 + -1x4 4x2 + -3x3 + -1x4 = x4 + -1x4 Combine like terms: x4 + -1x4 = 0 4x2 + -3x3 + -1x4 = 0 Factor out the Greatest Common Factor (GCF), 'x2'. x2(4 + -3x + -1x2) = 0 Factor a trinomial. x2((1 + -1x)(4 + x)) = 0Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
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 = 1Subproblem 3
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Solution
x = {0, 1, -4}
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