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Simplifying (6x3 + 3x)(x2 + 4) = 0 Reorder the terms: (3x + 6x3)(x2 + 4) = 0 Reorder the terms: (3x + 6x3)(4 + x2) = 0 Multiply (3x + 6x3) * (4 + x2) (3x * (4 + x2) + 6x3 * (4 + x2)) = 0 ((4 * 3x + x2 * 3x) + 6x3 * (4 + x2)) = 0 ((12x + 3x3) + 6x3 * (4 + x2)) = 0 (12x + 3x3 + (4 * 6x3 + x2 * 6x3)) = 0 (12x + 3x3 + (24x3 + 6x5)) = 0 Combine like terms: 3x3 + 24x3 = 27x3 (12x + 27x3 + 6x5) = 0 Solving 12x + 27x3 + 6x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x'. 3x(4 + 9x2 + 2x4) = 0 Factor a trinomial. 3x((4 + x2)(1 + 2x2)) = 0 Ignore the factor 3.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 '(4 + x2)' equal to zero and attempt to solve: Simplifying 4 + x2 = 0 Solving 4 + x2 = 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 + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x2 = 0 + -4 x2 = 0 + -4 Combine like terms: 0 + -4 = -4 x2 = -4 Simplifying x2 = -4 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(1 + 2x2)' equal to zero and attempt to solve: Simplifying 1 + 2x2 = 0 Solving 1 + 2x2 = 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 + 2x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x2 = 0 + -1 2x2 = 0 + -1 Combine like terms: 0 + -1 = -1 2x2 = -1 Divide each side by '2'. x2 = -0.5 Simplifying x2 = -0.5 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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