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Simplifying (5x3 + 5x)(x2 + 6) = 0 Reorder the terms: (5x + 5x3)(x2 + 6) = 0 Reorder the terms: (5x + 5x3)(6 + x2) = 0 Multiply (5x + 5x3) * (6 + x2) (5x * (6 + x2) + 5x3 * (6 + x2)) = 0 ((6 * 5x + x2 * 5x) + 5x3 * (6 + x2)) = 0 ((30x + 5x3) + 5x3 * (6 + x2)) = 0 (30x + 5x3 + (6 * 5x3 + x2 * 5x3)) = 0 (30x + 5x3 + (30x3 + 5x5)) = 0 Combine like terms: 5x3 + 30x3 = 35x3 (30x + 35x3 + 5x5) = 0 Solving 30x + 35x3 + 5x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5x'. 5x(6 + 7x2 + x4) = 0 Factor a trinomial. 5x((6 + x2)(1 + x2)) = 0 Ignore the factor 5.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 '(6 + x2)' equal to zero and attempt to solve: Simplifying 6 + x2 = 0 Solving 6 + x2 = 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 + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x2 = 0 + -6 x2 = 0 + -6 Combine like terms: 0 + -6 = -6 x2 = -6 Simplifying x2 = -6 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 + x2)' equal to zero and attempt to solve: Simplifying 1 + x2 = 0 Solving 1 + x2 = 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 + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = 0 + -1 x2 = 0 + -1 Combine like terms: 0 + -1 = -1 x2 = -1 Simplifying x2 = -1 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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