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Simplifying 5(2x3 + 9x) * 4(6x2 + 9) = 0 Reorder the terms: 5(9x + 2x3) * 4(6x2 + 9) = 0 Reorder the terms: 5(9x + 2x3) * 4(9 + 6x2) = 0 Reorder the terms for easier multiplication: 5 * 4(9x + 2x3)(9 + 6x2) = 0 Multiply 5 * 4 20(9x + 2x3)(9 + 6x2) = 0 Multiply (9x + 2x3) * (9 + 6x2) 20(9x * (9 + 6x2) + 2x3 * (9 + 6x2)) = 0 20((9 * 9x + 6x2 * 9x) + 2x3 * (9 + 6x2)) = 0 20((81x + 54x3) + 2x3 * (9 + 6x2)) = 0 20(81x + 54x3 + (9 * 2x3 + 6x2 * 2x3)) = 0 20(81x + 54x3 + (18x3 + 12x5)) = 0 Combine like terms: 54x3 + 18x3 = 72x3 20(81x + 72x3 + 12x5) = 0 (81x * 20 + 72x3 * 20 + 12x5 * 20) = 0 (1620x + 1440x3 + 240x5) = 0 Solving 1620x + 1440x3 + 240x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '60x'. 60x(27 + 24x2 + 4x4) = 0 Factor a trinomial. 60x((9 + 2x2)(3 + 2x2)) = 0 Ignore the factor 60.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 '(9 + 2x2)' equal to zero and attempt to solve: Simplifying 9 + 2x2 = 0 Solving 9 + 2x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 2x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 2x2 = 0 + -9 2x2 = 0 + -9 Combine like terms: 0 + -9 = -9 2x2 = -9 Divide each side by '2'. x2 = -4.5 Simplifying x2 = -4.5 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 '(3 + 2x2)' equal to zero and attempt to solve: Simplifying 3 + 2x2 = 0 Solving 3 + 2x2 = 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 + 2x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x2 = 0 + -3 2x2 = 0 + -3 Combine like terms: 0 + -3 = -3 2x2 = -3 Divide each side by '2'. x2 = -1.5 Simplifying x2 = -1.5 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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