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Simplifying 54(x2 + 3)(x2 + -9) = 0 Reorder the terms: 54(3 + x2)(x2 + -9) = 0 Reorder the terms: 54(3 + x2)(-9 + x2) = 0 Multiply (3 + x2) * (-9 + x2) 54(3(-9 + x2) + x2(-9 + x2)) = 0 54((-9 * 3 + x2 * 3) + x2(-9 + x2)) = 0 54((-27 + 3x2) + x2(-9 + x2)) = 0 54(-27 + 3x2 + (-9 * x2 + x2 * x2)) = 0 54(-27 + 3x2 + (-9x2 + x4)) = 0 Combine like terms: 3x2 + -9x2 = -6x2 54(-27 + -6x2 + x4) = 0 (-27 * 54 + -6x2 * 54 + x4 * 54) = 0 (-1458 + -324x2 + 54x4) = 0 Solving -1458 + -324x2 + 54x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '54'. 54(-27 + -6x2 + x4) = 0 Factor a trinomial. 54((-3 + -1x2)(9 + -1x2)) = 0 Factor a difference between two squares. 54((-3 + -1x2)((3 + x)(3 + -1x))) = 0 Ignore the factor 54.Subproblem 1
Set the factor '(-3 + -1x2)' equal to zero and attempt to solve: Simplifying -3 + -1x2 = 0 Solving -3 + -1x2 = 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 + -1x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x2 = 0 + 3 -1x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -1x2 = 3 Divide each side by '-1'. x2 = -3 Simplifying x2 = -3 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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