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Simplifying 0 = 4x4 + -12x3 + -72x2 Reorder the terms: 0 = -72x2 + -12x3 + 4x4 Solving 0 = -72x2 + -12x3 + 4x4 Solving for variable 'x'. Remove the zero: 72x2 + 12x3 + -4x4 = -72x2 + -12x3 + 4x4 + 72x2 + 12x3 + -4x4 Reorder the terms: 72x2 + 12x3 + -4x4 = -72x2 + 72x2 + -12x3 + 12x3 + 4x4 + -4x4 Combine like terms: -72x2 + 72x2 = 0 72x2 + 12x3 + -4x4 = 0 + -12x3 + 12x3 + 4x4 + -4x4 72x2 + 12x3 + -4x4 = -12x3 + 12x3 + 4x4 + -4x4 Combine like terms: -12x3 + 12x3 = 0 72x2 + 12x3 + -4x4 = 0 + 4x4 + -4x4 72x2 + 12x3 + -4x4 = 4x4 + -4x4 Combine like terms: 4x4 + -4x4 = 0 72x2 + 12x3 + -4x4 = 0 Factor out the Greatest Common Factor (GCF), '4x2'. 4x2(18 + 3x + -1x2) = 0 Factor a trinomial. 4x2((6 + -1x)(3 + x)) = 0 Ignore the factor 4.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 '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Subproblem 3
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 = -3Solution
x = {0, 6, -3}
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