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Simplifying (x2 + -9)(2x2 + 3) = 0 Reorder the terms: (-9 + x2)(2x2 + 3) = 0 Reorder the terms: (-9 + x2)(3 + 2x2) = 0 Multiply (-9 + x2) * (3 + 2x2) (-9(3 + 2x2) + x2(3 + 2x2)) = 0 ((3 * -9 + 2x2 * -9) + x2(3 + 2x2)) = 0 ((-27 + -18x2) + x2(3 + 2x2)) = 0 (-27 + -18x2 + (3 * x2 + 2x2 * x2)) = 0 (-27 + -18x2 + (3x2 + 2x4)) = 0 Combine like terms: -18x2 + 3x2 = -15x2 (-27 + -15x2 + 2x4) = 0 Solving -27 + -15x2 + 2x4 = 0 Solving for variable 'x'. Factor a trinomial. (-3 + -2x2)(9 + -1x2) = 0 Factor a difference between two squares. (-3 + -2x2)((3 + x)(3 + -1x)) = 0Subproblem 1
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.Subproblem 2
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 = -3Subproblem 3
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {-3, 3}
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