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Simplifying 0 = 4x4 + 12x3 + 9x2 Reorder the terms: 0 = 9x2 + 12x3 + 4x4 Solving 0 = 9x2 + 12x3 + 4x4 Solving for variable 'x'. Remove the zero: -9x2 + -12x3 + -4x4 = 9x2 + 12x3 + 4x4 + -9x2 + -12x3 + -4x4 Reorder the terms: -9x2 + -12x3 + -4x4 = 9x2 + -9x2 + 12x3 + -12x3 + 4x4 + -4x4 Combine like terms: 9x2 + -9x2 = 0 -9x2 + -12x3 + -4x4 = 0 + 12x3 + -12x3 + 4x4 + -4x4 -9x2 + -12x3 + -4x4 = 12x3 + -12x3 + 4x4 + -4x4 Combine like terms: 12x3 + -12x3 = 0 -9x2 + -12x3 + -4x4 = 0 + 4x4 + -4x4 -9x2 + -12x3 + -4x4 = 4x4 + -4x4 Combine like terms: 4x4 + -4x4 = 0 -9x2 + -12x3 + -4x4 = 0 Factor out the Greatest Common Factor (GCF), '-1x2'. -1x2(9 + 12x + 4x2) = 0 Factor a trinomial. -1x2((3 + 2x)(3 + 2x)) = 0 Ignore the factor -1.Subproblem 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 '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 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 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5Subproblem 3
Set the factor '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 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 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5Solution
x = {0, -1.5, -1.5}
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