lg(x^2-9x+52)=lg(5x+4)

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Solution for lg(x^2-9x+52)=lg(5x+4) equation: 


Simplifying
lg(x2 + -9x + 52) = lg(5x + 4)

Reorder the terms:
gl(52 + -9x + x2) = lg(5x + 4)
(52 * gl + -9x * gl + x2 * gl) = lg(5x + 4)
(52gl + -9glx + glx2) = lg(5x + 4)

Reorder the terms:
52gl + -9glx + glx2 = gl(4 + 5x)
52gl + -9glx + glx2 = (4 * gl + 5x * gl)
52gl + -9glx + glx2 = (4gl + 5glx)

Solving
52gl + -9glx + glx2 = 4gl + 5glx

Solving for variable 'g'.

Move all terms containing g to the left, all other terms to the right.

Add '-4gl' to each side of the equation.
52gl + -9glx + -4gl + glx2 = 4gl + -4gl + 5glx

Reorder the terms:
52gl + -4gl + -9glx + glx2 = 4gl + -4gl + 5glx

Combine like terms: 52gl + -4gl = 48gl
48gl + -9glx + glx2 = 4gl + -4gl + 5glx

Combine like terms: 4gl + -4gl = 0
48gl + -9glx + glx2 = 0 + 5glx
48gl + -9glx + glx2 = 5glx

Add '-5glx' to each side of the equation.
48gl + -9glx + -5glx + glx2 = 5glx + -5glx

Combine like terms: -9glx + -5glx = -14glx
48gl + -14glx + glx2 = 5glx + -5glx

Combine like terms: 5glx + -5glx = 0
48gl + -14glx + glx2 = 0

Factor out the Greatest Common Factor (GCF), 'gl'.
gl(48 + -14x + x2) = 0

Factor a trinomial.
gl((6 + -1x)(8 + -1x)) = 0


Subproblem 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 '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

Move all terms containing g to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Add 'x' to each side of the equation.
-1x + x = -6 + x

Combine like terms: -1x + x = 0
0 = -6 + x

Simplifying
0 = -6 + x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 3
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

Move all terms containing g to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Add 'x' to each side of the equation.
-1x + x = -8 + x

Combine like terms: -1x + x = 0
0 = -8 + x

Simplifying
0 = -8 + x

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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