log(4x^2+5x)=log(34x+63)

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Solution for log(4x^2+5x)=log(34x+63) equation: 


Simplifying
log(4x2 + 5x) = log(34x + 63)

Reorder the terms:
glo(5x + 4x2) = log(34x + 63)
(5x * glo + 4x2 * glo) = log(34x + 63)
(5glox + 4glox2) = log(34x + 63)

Reorder the terms:
5glox + 4glox2 = glo(63 + 34x)
5glox + 4glox2 = (63 * glo + 34x * glo)
5glox + 4glox2 = (63glo + 34glox)

Solving
5glox + 4glox2 = 63glo + 34glox

Solving for variable 'g'.

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

Add '-63glo' to each side of the equation.
5glox + -63glo + 4glox2 = 63glo + -63glo + 34glox

Reorder the terms:
-63glo + 5glox + 4glox2 = 63glo + -63glo + 34glox

Combine like terms: 63glo + -63glo = 0
-63glo + 5glox + 4glox2 = 0 + 34glox
-63glo + 5glox + 4glox2 = 34glox

Add '-34glox' to each side of the equation.
-63glo + 5glox + -34glox + 4glox2 = 34glox + -34glox

Combine like terms: 5glox + -34glox = -29glox
-63glo + -29glox + 4glox2 = 34glox + -34glox

Combine like terms: 34glox + -34glox = 0
-63glo + -29glox + 4glox2 = 0

Factor out the Greatest Common Factor (GCF), 'glo'.
glo(-63 + -29x + 4x2) = 0

Factor a trinomial.
glo((-7 + -4x)(9 + -1x)) = 0


Subproblem 1
Set the factor 'glo' equal to zero and attempt to solve:

Simplifying
glo = 0

Solving
glo = 0

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

Simplifying
glo = 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 '(-7 + -4x)' equal to zero and attempt to solve:

Simplifying
-7 + -4x = 0

Solving
-7 + -4x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -4x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -4x = 0 + 7
-4x = 0 + 7

Combine like terms: 0 + 7 = 7
-4x = 7

Add '4x' to each side of the equation.
-4x + 4x = 7 + 4x

Combine like terms: -4x + 4x = 0
0 = 7 + 4x

Simplifying
0 = 7 + 4x

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 '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Add 'x' to each side of the equation.
-1x + x = -9 + x

Combine like terms: -1x + x = 0
0 = -9 + x

Simplifying
0 = -9 + 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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