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Simplifying (x + 6)(x + 6)(x + -6)(x + -6) = 0 Reorder the terms: (6 + x)(x + 6)(x + -6)(x + -6) = 0 Reorder the terms: (6 + x)(6 + x)(x + -6)(x + -6) = 0 Reorder the terms: (6 + x)(6 + x)(-6 + x)(x + -6) = 0 Reorder the terms: (6 + x)(6 + x)(-6 + x)(-6 + x) = 0 Multiply (6 + x) * (6 + x) (6(6 + x) + x(6 + x))(-6 + x)(-6 + x) = 0 ((6 * 6 + x * 6) + x(6 + x))(-6 + x)(-6 + x) = 0 ((36 + 6x) + x(6 + x))(-6 + x)(-6 + x) = 0 (36 + 6x + (6 * x + x * x))(-6 + x)(-6 + x) = 0 (36 + 6x + (6x + x2))(-6 + x)(-6 + x) = 0 Combine like terms: 6x + 6x = 12x (36 + 12x + x2)(-6 + x)(-6 + x) = 0 Multiply (36 + 12x + x2) * (-6 + x) (36(-6 + x) + 12x * (-6 + x) + x2(-6 + x))(-6 + x) = 0 ((-6 * 36 + x * 36) + 12x * (-6 + x) + x2(-6 + x))(-6 + x) = 0 ((-216 + 36x) + 12x * (-6 + x) + x2(-6 + x))(-6 + x) = 0 (-216 + 36x + (-6 * 12x + x * 12x) + x2(-6 + x))(-6 + x) = 0 (-216 + 36x + (-72x + 12x2) + x2(-6 + x))(-6 + x) = 0 (-216 + 36x + -72x + 12x2 + (-6 * x2 + x * x2))(-6 + x) = 0 (-216 + 36x + -72x + 12x2 + (-6x2 + x3))(-6 + x) = 0 Combine like terms: 36x + -72x = -36x (-216 + -36x + 12x2 + -6x2 + x3)(-6 + x) = 0 Combine like terms: 12x2 + -6x2 = 6x2 (-216 + -36x + 6x2 + x3)(-6 + x) = 0 Multiply (-216 + -36x + 6x2 + x3) * (-6 + x) (-216(-6 + x) + -36x * (-6 + x) + 6x2 * (-6 + x) + x3(-6 + x)) = 0 ((-6 * -216 + x * -216) + -36x * (-6 + x) + 6x2 * (-6 + x) + x3(-6 + x)) = 0 ((1296 + -216x) + -36x * (-6 + x) + 6x2 * (-6 + x) + x3(-6 + x)) = 0 (1296 + -216x + (-6 * -36x + x * -36x) + 6x2 * (-6 + x) + x3(-6 + x)) = 0 (1296 + -216x + (216x + -36x2) + 6x2 * (-6 + x) + x3(-6 + x)) = 0 (1296 + -216x + 216x + -36x2 + (-6 * 6x2 + x * 6x2) + x3(-6 + x)) = 0 (1296 + -216x + 216x + -36x2 + (-36x2 + 6x3) + x3(-6 + x)) = 0 (1296 + -216x + 216x + -36x2 + -36x2 + 6x3 + (-6 * x3 + x * x3)) = 0 (1296 + -216x + 216x + -36x2 + -36x2 + 6x3 + (-6x3 + x4)) = 0 Combine like terms: -216x + 216x = 0 (1296 + 0 + -36x2 + -36x2 + 6x3 + -6x3 + x4) = 0 (1296 + -36x2 + -36x2 + 6x3 + -6x3 + x4) = 0 Combine like terms: -36x2 + -36x2 = -72x2 (1296 + -72x2 + 6x3 + -6x3 + x4) = 0 Combine like terms: 6x3 + -6x3 = 0 (1296 + -72x2 + 0 + x4) = 0 (1296 + -72x2 + x4) = 0 Solving 1296 + -72x2 + x4 = 0 Solving for variable 'x'. Factor a trinomial. (36 + -1x2)(36 + -1x2) = 0 Factor a difference between two squares. ((6 + x)(6 + -1x))(36 + -1x2) = 0 Factor a difference between two squares. ((6 + x)(6 + -1x))(6 + x)(6 + -1x) = 0Subproblem 1
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 2
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 = 6Subproblem 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 = {-6, 6, -6, 6}
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