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Simplifying 0 = 2(x32 + 6x16 + -7) Reorder the terms: 0 = 2(-7 + 6x16 + x32) 0 = (-7 * 2 + 6x16 * 2 + x32 * 2) 0 = (-14 + 12x16 + 2x32) Solving 0 = -14 + 12x16 + 2x32 Solving for variable 'x'. Combine like terms: 0 + 14 = 14 14 + -12x16 + -2x32 = -14 + 12x16 + 2x32 + 14 + -12x16 + -2x32 Reorder the terms: 14 + -12x16 + -2x32 = -14 + 14 + 12x16 + -12x16 + 2x32 + -2x32 Combine like terms: -14 + 14 = 0 14 + -12x16 + -2x32 = 0 + 12x16 + -12x16 + 2x32 + -2x32 14 + -12x16 + -2x32 = 12x16 + -12x16 + 2x32 + -2x32 Combine like terms: 12x16 + -12x16 = 0 14 + -12x16 + -2x32 = 0 + 2x32 + -2x32 14 + -12x16 + -2x32 = 2x32 + -2x32 Combine like terms: 2x32 + -2x32 = 0 14 + -12x16 + -2x32 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(7 + -6x16 + -1x32) = 0 Factor a trinomial. 2((1 + -1x16)(7 + x16)) = 0 Factor a difference between two squares. 2(((1 + x8)(1 + -1x8))(7 + x16)) = 0 Factor a difference between two squares. 2(((1 + x8)((1 + x4)(1 + -1x4)))(7 + x16)) = 0 Factor a difference between two squares. 2(((1 + x8)((1 + x4)((1 + x2)(1 + -1x2))))(7 + x16)) = 0 Factor a difference between two squares. 2(((1 + x8)((1 + x4)((1 + x2)((1 + x)(1 + -1x)))))(7 + x16)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + x16)' equal to zero and attempt to solve: Simplifying 7 + x16 = 0 Solving 7 + x16 = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x16 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x16 = 0 + -7 x16 = 0 + -7 Combine like terms: 0 + -7 = -7 x16 = -7 Simplifying x16 = -7 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 '(1 + x8)' equal to zero and attempt to solve: Simplifying 1 + x8 = 0 Solving 1 + x8 = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x8 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x8 = 0 + -1 x8 = 0 + -1 Combine like terms: 0 + -1 = -1 x8 = -1 Simplifying x8 = -1 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(1 + x4)' equal to zero and attempt to solve: Simplifying 1 + x4 = 0 Solving 1 + x4 = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x4 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x4 = 0 + -1 x4 = 0 + -1 Combine like terms: 0 + -1 = -1 x4 = -1 Simplifying x4 = -1 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 4
Set the factor '(1 + x2)' equal to zero and attempt to solve: Simplifying 1 + x2 = 0 Solving 1 + x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = 0 + -1 x2 = 0 + -1 Combine like terms: 0 + -1 = -1 x2 = -1 Simplifying x2 = -1 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 5
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Subproblem 6
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {-1, 1}
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