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Simplifying lg(x2 + -2kx) = lg(8x + -6k + -3) Reorder the terms: gl(-2kx + x2) = lg(8x + -6k + -3) (-2kx * gl + x2 * gl) = lg(8x + -6k + -3) (-2gklx + glx2) = lg(8x + -6k + -3) Reorder the terms: -2gklx + glx2 = gl(-3 + -6k + 8x) -2gklx + glx2 = (-3 * gl + -6k * gl + 8x * gl) Reorder the terms: -2gklx + glx2 = (-6gkl + -3gl + 8glx) -2gklx + glx2 = (-6gkl + -3gl + 8glx) Solving -2gklx + glx2 = -6gkl + -3gl + 8glx Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '6gkl' to each side of the equation. -2gklx + 6gkl + glx2 = -6gkl + -3gl + 6gkl + 8glx Reorder the terms: 6gkl + -2gklx + glx2 = -6gkl + -3gl + 6gkl + 8glx Reorder the terms: 6gkl + -2gklx + glx2 = -6gkl + 6gkl + -3gl + 8glx Combine like terms: -6gkl + 6gkl = 0 6gkl + -2gklx + glx2 = 0 + -3gl + 8glx 6gkl + -2gklx + glx2 = -3gl + 8glx Add '3gl' to each side of the equation. 6gkl + -2gklx + 3gl + glx2 = -3gl + 3gl + 8glx Combine like terms: -3gl + 3gl = 0 6gkl + -2gklx + 3gl + glx2 = 0 + 8glx 6gkl + -2gklx + 3gl + glx2 = 8glx Add '-8glx' to each side of the equation. 6gkl + -2gklx + 3gl + -8glx + glx2 = 8glx + -8glx Combine like terms: 8glx + -8glx = 0 6gkl + -2gklx + 3gl + -8glx + glx2 = 0 Factor out the Greatest Common Factor (GCF), 'gl'. gl(6k + -2kx + 3 + -8x + x2) = 0Subproblem 1
Set the factor 'gl' equal to zero and attempt to solve: Simplifying gl = 0 Solving gl = 0 Move all terms containing g to the left, all other terms to the right. Simplifying gl = 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 '(6k + -2kx + 3 + -8x + x2)' equal to zero and attempt to solve: Simplifying 6k + -2kx + 3 + -8x + x2 = 0 Reorder the terms: 3 + 6k + -2kx + -8x + x2 = 0 Solving 3 + 6k + -2kx + -8x + x2 = 0 Move all terms containing g to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + 6k + -2kx + -8x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 6k + -2kx + -8x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 6k + -2kx + -8x + x2 = 0 + -3 6k + -2kx + -8x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 6k + -2kx + -8x + x2 = -3 Add '-6k' to each side of the equation. 6k + -2kx + -8x + -6k + x2 = -3 + -6k Reorder the terms: 6k + -6k + -2kx + -8x + x2 = -3 + -6k Combine like terms: 6k + -6k = 0 0 + -2kx + -8x + x2 = -3 + -6k -2kx + -8x + x2 = -3 + -6k Add '2kx' to each side of the equation. -2kx + -8x + 2kx + x2 = -3 + -6k + 2kx Reorder the terms: -2kx + 2kx + -8x + x2 = -3 + -6k + 2kx Combine like terms: -2kx + 2kx = 0 0 + -8x + x2 = -3 + -6k + 2kx -8x + x2 = -3 + -6k + 2kx Add '8x' to each side of the equation. -8x + 8x + x2 = -3 + -6k + 2kx + 8x Combine like terms: -8x + 8x = 0 0 + x2 = -3 + -6k + 2kx + 8x x2 = -3 + -6k + 2kx + 8x Add '-1x2' to each side of the equation. x2 + -1x2 = -3 + -6k + 2kx + 8x + -1x2 Combine like terms: x2 + -1x2 = 0 0 = -3 + -6k + 2kx + 8x + -1x2 Simplifying 0 = -3 + -6k + 2kx + 8x + -1x2 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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