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Simplifying 0 = 6x4 + -21x3 + -12x2 Reorder the terms: 0 = -12x2 + -21x3 + 6x4 Solving 0 = -12x2 + -21x3 + 6x4 Solving for variable 'x'. Remove the zero: 12x2 + 21x3 + -6x4 = -12x2 + -21x3 + 6x4 + 12x2 + 21x3 + -6x4 Reorder the terms: 12x2 + 21x3 + -6x4 = -12x2 + 12x2 + -21x3 + 21x3 + 6x4 + -6x4 Combine like terms: -12x2 + 12x2 = 0 12x2 + 21x3 + -6x4 = 0 + -21x3 + 21x3 + 6x4 + -6x4 12x2 + 21x3 + -6x4 = -21x3 + 21x3 + 6x4 + -6x4 Combine like terms: -21x3 + 21x3 = 0 12x2 + 21x3 + -6x4 = 0 + 6x4 + -6x4 12x2 + 21x3 + -6x4 = 6x4 + -6x4 Combine like terms: 6x4 + -6x4 = 0 12x2 + 21x3 + -6x4 = 0 Factor out the Greatest Common Factor (GCF), '3x2'. 3x2(4 + 7x + -2x2) = 0 Factor a trinomial. 3x2((4 + -1x)(1 + 2x)) = 0 Ignore the factor 3.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 '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 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 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Subproblem 3
Set the factor '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 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 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Divide each side by '2'. x = -0.5 Simplifying x = -0.5Solution
x = {0, 4, -0.5}
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