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Simplifying (x2 + 12x + 36)(x2 + -12x + 36) = 0 Reorder the terms: (36 + 12x + x2)(x2 + -12x + 36) = 0 Reorder the terms: (36 + 12x + x2)(36 + -12x + x2) = 0 Multiply (36 + 12x + x2) * (36 + -12x + x2) (36(36 + -12x + x2) + 12x * (36 + -12x + x2) + x2(36 + -12x + x2)) = 0 ((36 * 36 + -12x * 36 + x2 * 36) + 12x * (36 + -12x + x2) + x2(36 + -12x + x2)) = 0 ((1296 + -432x + 36x2) + 12x * (36 + -12x + x2) + x2(36 + -12x + x2)) = 0 (1296 + -432x + 36x2 + (36 * 12x + -12x * 12x + x2 * 12x) + x2(36 + -12x + x2)) = 0 (1296 + -432x + 36x2 + (432x + -144x2 + 12x3) + x2(36 + -12x + x2)) = 0 (1296 + -432x + 36x2 + 432x + -144x2 + 12x3 + (36 * x2 + -12x * x2 + x2 * x2)) = 0 (1296 + -432x + 36x2 + 432x + -144x2 + 12x3 + (36x2 + -12x3 + x4)) = 0 Reorder the terms: (1296 + -432x + 432x + 36x2 + -144x2 + 36x2 + 12x3 + -12x3 + x4) = 0 Combine like terms: -432x + 432x = 0 (1296 + 0 + 36x2 + -144x2 + 36x2 + 12x3 + -12x3 + x4) = 0 (1296 + 36x2 + -144x2 + 36x2 + 12x3 + -12x3 + x4) = 0 Combine like terms: 36x2 + -144x2 = -108x2 (1296 + -108x2 + 36x2 + 12x3 + -12x3 + x4) = 0 Combine like terms: -108x2 + 36x2 = -72x2 (1296 + -72x2 + 12x3 + -12x3 + x4) = 0 Combine like terms: 12x3 + -12x3 = 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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