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Simplifying 0 = x7 + 4x6 + 3x5 Reorder the terms: 0 = 3x5 + 4x6 + x7 Solving 0 = 3x5 + 4x6 + x7 Solving for variable 'x'. Remove the zero: -3x5 + -4x6 + -1x7 = 3x5 + 4x6 + x7 + -3x5 + -4x6 + -1x7 Reorder the terms: -3x5 + -4x6 + -1x7 = 3x5 + -3x5 + 4x6 + -4x6 + x7 + -1x7 Combine like terms: 3x5 + -3x5 = 0 -3x5 + -4x6 + -1x7 = 0 + 4x6 + -4x6 + x7 + -1x7 -3x5 + -4x6 + -1x7 = 4x6 + -4x6 + x7 + -1x7 Combine like terms: 4x6 + -4x6 = 0 -3x5 + -4x6 + -1x7 = 0 + x7 + -1x7 -3x5 + -4x6 + -1x7 = x7 + -1x7 Combine like terms: x7 + -1x7 = 0 -3x5 + -4x6 + -1x7 = 0 Factor out the Greatest Common Factor (GCF), '-1x5'. -1x5(3 + 4x + x2) = 0 Factor a trinomial. -1x5((3 + x)(1 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor 'x5' equal to zero and attempt to solve: Simplifying x5 = 0 Solving x5 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x5 = 0 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 '(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 = -1Solution
x = {-3, -1}
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