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Simplifying (x + -6)(x + 6)(x + 3)(x + -3) = 0 Reorder the terms: (-6 + x)(x + 6)(x + 3)(x + -3) = 0 Reorder the terms: (-6 + x)(6 + x)(x + 3)(x + -3) = 0 Reorder the terms: (-6 + x)(6 + x)(3 + x)(x + -3) = 0 Reorder the terms: (-6 + x)(6 + x)(3 + x)(-3 + x) = 0 Multiply (-6 + x) * (6 + x) (-6(6 + x) + x(6 + x))(3 + x)(-3 + x) = 0 ((6 * -6 + x * -6) + x(6 + x))(3 + x)(-3 + x) = 0 ((-36 + -6x) + x(6 + x))(3 + x)(-3 + x) = 0 (-36 + -6x + (6 * x + x * x))(3 + x)(-3 + x) = 0 (-36 + -6x + (6x + x2))(3 + x)(-3 + x) = 0 Combine like terms: -6x + 6x = 0 (-36 + 0 + x2)(3 + x)(-3 + x) = 0 (-36 + x2)(3 + x)(-3 + x) = 0 Multiply (-36 + x2) * (3 + x) (-36(3 + x) + x2(3 + x))(-3 + x) = 0 ((3 * -36 + x * -36) + x2(3 + x))(-3 + x) = 0 ((-108 + -36x) + x2(3 + x))(-3 + x) = 0 (-108 + -36x + (3 * x2 + x * x2))(-3 + x) = 0 (-108 + -36x + (3x2 + x3))(-3 + x) = 0 (-108 + -36x + 3x2 + x3)(-3 + x) = 0 Multiply (-108 + -36x + 3x2 + x3) * (-3 + x) (-108(-3 + x) + -36x * (-3 + x) + 3x2 * (-3 + x) + x3(-3 + x)) = 0 ((-3 * -108 + x * -108) + -36x * (-3 + x) + 3x2 * (-3 + x) + x3(-3 + x)) = 0 ((324 + -108x) + -36x * (-3 + x) + 3x2 * (-3 + x) + x3(-3 + x)) = 0 (324 + -108x + (-3 * -36x + x * -36x) + 3x2 * (-3 + x) + x3(-3 + x)) = 0 (324 + -108x + (108x + -36x2) + 3x2 * (-3 + x) + x3(-3 + x)) = 0 (324 + -108x + 108x + -36x2 + (-3 * 3x2 + x * 3x2) + x3(-3 + x)) = 0 (324 + -108x + 108x + -36x2 + (-9x2 + 3x3) + x3(-3 + x)) = 0 (324 + -108x + 108x + -36x2 + -9x2 + 3x3 + (-3 * x3 + x * x3)) = 0 (324 + -108x + 108x + -36x2 + -9x2 + 3x3 + (-3x3 + x4)) = 0 Combine like terms: -108x + 108x = 0 (324 + 0 + -36x2 + -9x2 + 3x3 + -3x3 + x4) = 0 (324 + -36x2 + -9x2 + 3x3 + -3x3 + x4) = 0 Combine like terms: -36x2 + -9x2 = -45x2 (324 + -45x2 + 3x3 + -3x3 + x4) = 0 Combine like terms: 3x3 + -3x3 = 0 (324 + -45x2 + 0 + x4) = 0 (324 + -45x2 + x4) = 0 Solving 324 + -45x2 + x4 = 0 Solving for variable 'x'. Factor a trinomial. (9 + -1x2)(36 + -1x2) = 0 Factor a difference between two squares. ((3 + x)(3 + -1x))(36 + -1x2) = 0 Factor a difference between two squares. ((6 + x)(6 + -1x))(3 + x)(3 + -1x) = 0Subproblem 1
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 2
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 = 3Subproblem 3
Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 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 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6Subproblem 4
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 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 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {-3, 3, -6, 6}
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