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Simplifying n(2x + -3) + ln(x + 4) = ln(2x2 + 11) Reorder the terms: n(-3 + 2x) + ln(x + 4) = ln(2x2 + 11) (-3 * n + 2x * n) + ln(x + 4) = ln(2x2 + 11) (-3n + 2nx) + ln(x + 4) = ln(2x2 + 11) Reorder the terms: -3n + 2nx + ln(4 + x) = ln(2x2 + 11) -3n + 2nx + (4 * ln + x * ln) = ln(2x2 + 11) -3n + 2nx + (4ln + lnx) = ln(2x2 + 11) Reorder the terms: 4ln + lnx + -3n + 2nx = ln(2x2 + 11) Reorder the terms: 4ln + lnx + -3n + 2nx = ln(11 + 2x2) 4ln + lnx + -3n + 2nx = (11 * ln + 2x2 * ln) 4ln + lnx + -3n + 2nx = (11ln + 2lnx2) Solving 4ln + lnx + -3n + 2nx = 11ln + 2lnx2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-11ln' to each side of the equation. 4ln + lnx + -3n + -11ln + 2nx = 11ln + -11ln + 2lnx2 Reorder the terms: 4ln + -11ln + lnx + -3n + 2nx = 11ln + -11ln + 2lnx2 Combine like terms: 4ln + -11ln = -7ln -7ln + lnx + -3n + 2nx = 11ln + -11ln + 2lnx2 Combine like terms: 11ln + -11ln = 0 -7ln + lnx + -3n + 2nx = 0 + 2lnx2 -7ln + lnx + -3n + 2nx = 2lnx2 Add '-2lnx2' to each side of the equation. -7ln + lnx + -3n + -2lnx2 + 2nx = 2lnx2 + -2lnx2 Reorder the terms: -7ln + lnx + -2lnx2 + -3n + 2nx = 2lnx2 + -2lnx2 Combine like terms: 2lnx2 + -2lnx2 = 0 -7ln + lnx + -2lnx2 + -3n + 2nx = 0 Add '3n' to each side of the equation. -7ln + lnx + -2lnx2 + -3n + 3n + 2nx = 0 + 3n Combine like terms: -3n + 3n = 0 -7ln + lnx + -2lnx2 + 0 + 2nx = 0 + 3n -7ln + lnx + -2lnx2 + 2nx = 0 + 3n Remove the zero: -7ln + lnx + -2lnx2 + 2nx = 3n Add '-2nx' to each side of the equation. -7ln + lnx + -2lnx2 + 2nx + -2nx = 3n + -2nx Combine like terms: 2nx + -2nx = 0 -7ln + lnx + -2lnx2 + 0 = 3n + -2nx -7ln + lnx + -2lnx2 = 3n + -2nx Reorder the terms: -7ln + lnx + -2lnx2 + -3n + 2nx = 3n + -3n + -2nx + 2nx Combine like terms: 3n + -3n = 0 -7ln + lnx + -2lnx2 + -3n + 2nx = 0 + -2nx + 2nx -7ln + lnx + -2lnx2 + -3n + 2nx = -2nx + 2nx Combine like terms: -2nx + 2nx = 0 -7ln + lnx + -2lnx2 + -3n + 2nx = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-7l + lx + -2lx2 + -3 + 2x) = 0Subproblem 1
Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing l to the left, all other terms to the right. Add '-1n' to each side of the equation. n + -1n = 0 + -1n Remove the zero: 0 = -1n Simplifying 0 = -1n 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 '(-7l + lx + -2lx2 + -3 + 2x)' equal to zero and attempt to solve: Simplifying -7l + lx + -2lx2 + -3 + 2x = 0 Reorder the terms: -3 + -7l + lx + -2lx2 + 2x = 0 Solving -3 + -7l + lx + -2lx2 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '3' to each side of the equation. -3 + -7l + lx + -2lx2 + 3 + 2x = 0 + 3 Reorder the terms: -3 + 3 + -7l + lx + -2lx2 + 2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -7l + lx + -2lx2 + 2x = 0 + 3 -7l + lx + -2lx2 + 2x = 0 + 3 Combine like terms: 0 + 3 = 3 -7l + lx + -2lx2 + 2x = 3 Add '-2x' to each side of the equation. -7l + lx + -2lx2 + 2x + -2x = 3 + -2x Combine like terms: 2x + -2x = 0 -7l + lx + -2lx2 + 0 = 3 + -2x -7l + lx + -2lx2 = 3 + -2x 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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