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Simplifying lg2(5 + -3x) = lg2(20 + -12x) (5 * g2l + -3x * g2l) = lg2(20 + -12x) (5g2l + -3g2lx) = lg2(20 + -12x) 5g2l + -3g2lx = (20 * g2l + -12x * g2l) 5g2l + -3g2lx = (20g2l + -12g2lx) Solving 5g2l + -3g2lx = 20g2l + -12g2lx Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-20g2l' to each side of the equation. 5g2l + -20g2l + -3g2lx = 20g2l + -20g2l + -12g2lx Combine like terms: 5g2l + -20g2l = -15g2l -15g2l + -3g2lx = 20g2l + -20g2l + -12g2lx Combine like terms: 20g2l + -20g2l = 0 -15g2l + -3g2lx = 0 + -12g2lx -15g2l + -3g2lx = -12g2lx Add '12g2lx' to each side of the equation. -15g2l + -3g2lx + 12g2lx = -12g2lx + 12g2lx Combine like terms: -3g2lx + 12g2lx = 9g2lx -15g2l + 9g2lx = -12g2lx + 12g2lx Combine like terms: -12g2lx + 12g2lx = 0 -15g2l + 9g2lx = 0 Factor out the Greatest Common Factor (GCF), '3g2l'. 3g2l(-5 + 3x) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'g2l' equal to zero and attempt to solve: Simplifying g2l = 0 Solving g2l = 0 Move all terms containing g to the left, all other terms to the right. Simplifying g2l = 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 '(-5 + 3x)' equal to zero and attempt to solve: Simplifying -5 + 3x = 0 Solving -5 + 3x = 0 Move all terms containing g to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + 3x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 3x = 0 + 5 3x = 0 + 5 Combine like terms: 0 + 5 = 5 3x = 5 Add '-3x' to each side of the equation. 3x + -3x = 5 + -3x Combine like terms: 3x + -3x = 0 0 = 5 + -3x Simplifying 0 = 5 + -3x 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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