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Simplifying 3e2x + 12 = 42 Reorder the terms: 12 + 3e2x = 42 Solving 12 + 3e2x = 42 Solving for variable 'e'. Move all terms containing e to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + 3e2x = 42 + -12 Combine like terms: 12 + -12 = 0 0 + 3e2x = 42 + -12 3e2x = 42 + -12 Combine like terms: 42 + -12 = 30 3e2x = 30 Divide each side by '3x'. e2 = 10x-1 Simplifying e2 = 10x-1 Combine like terms: 10x-1 + -10x-1 = 0 e2 + -10x-1 = 0 Factor out the Greatest Common Factor (GCF), 'x-1'. x-1(e2x + -10) = 0Subproblem 1
Set the factor 'x-1' equal to zero and attempt to solve: Simplifying x-1 = 0 Solving x-1 = 0 Move all terms containing e to the left, all other terms to the right. Add '-1x-1' to each side of the equation. x-1 + -1x-1 = 0 + -1x-1 Remove the zero: 0 = -1x-1 Simplifying 0 = -1x-1 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 '(e2x + -10)' equal to zero and attempt to solve: Simplifying e2x + -10 = 0 Reorder the terms: -10 + e2x = 0 Solving -10 + e2x = 0 Move all terms containing e to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + e2x = 0 + 10 Combine like terms: -10 + 10 = 0 0 + e2x = 0 + 10 e2x = 0 + 10 Combine like terms: 0 + 10 = 10 e2x = 10 Divide each side by 'x'. e2 = 10x-1 Simplifying e2 = 10x-1 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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