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Simplifying 0 = 10x7 + 34x6 + 12x5 Reorder the terms: 0 = 12x5 + 34x6 + 10x7 Solving 0 = 12x5 + 34x6 + 10x7 Solving for variable 'x'. Remove the zero: -12x5 + -34x6 + -10x7 = 12x5 + 34x6 + 10x7 + -12x5 + -34x6 + -10x7 Reorder the terms: -12x5 + -34x6 + -10x7 = 12x5 + -12x5 + 34x6 + -34x6 + 10x7 + -10x7 Combine like terms: 12x5 + -12x5 = 0 -12x5 + -34x6 + -10x7 = 0 + 34x6 + -34x6 + 10x7 + -10x7 -12x5 + -34x6 + -10x7 = 34x6 + -34x6 + 10x7 + -10x7 Combine like terms: 34x6 + -34x6 = 0 -12x5 + -34x6 + -10x7 = 0 + 10x7 + -10x7 -12x5 + -34x6 + -10x7 = 10x7 + -10x7 Combine like terms: 10x7 + -10x7 = 0 -12x5 + -34x6 + -10x7 = 0 Factor out the Greatest Common Factor (GCF), '-2x5'. -2x5(6 + 17x + 5x2) = 0 Factor a trinomial. -2x5((3 + x)(2 + 5x)) = 0 Ignore the factor -2.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 '(2 + 5x)' equal to zero and attempt to solve: Simplifying 2 + 5x = 0 Solving 2 + 5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 5x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5x = 0 + -2 5x = 0 + -2 Combine like terms: 0 + -2 = -2 5x = -2 Divide each side by '5'. x = -0.4 Simplifying x = -0.4Solution
x = {-3, -0.4}
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