log(2x^2+4x)=log(15x+40)

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Solution for log(2x^2+4x)=log(15x+40) equation: 


Simplifying
log(2x2 + 4x) = log(15x + 40)

Reorder the terms:
glo(4x + 2x2) = log(15x + 40)
(4x * glo + 2x2 * glo) = log(15x + 40)
(4glox + 2glox2) = log(15x + 40)

Reorder the terms:
4glox + 2glox2 = glo(40 + 15x)
4glox + 2glox2 = (40 * glo + 15x * glo)
4glox + 2glox2 = (40glo + 15glox)

Solving
4glox + 2glox2 = 40glo + 15glox

Solving for variable 'g'.

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

Add '-40glo' to each side of the equation.
4glox + -40glo + 2glox2 = 40glo + -40glo + 15glox

Reorder the terms:
-40glo + 4glox + 2glox2 = 40glo + -40glo + 15glox

Combine like terms: 40glo + -40glo = 0
-40glo + 4glox + 2glox2 = 0 + 15glox
-40glo + 4glox + 2glox2 = 15glox

Add '-15glox' to each side of the equation.
-40glo + 4glox + -15glox + 2glox2 = 15glox + -15glox

Combine like terms: 4glox + -15glox = -11glox
-40glo + -11glox + 2glox2 = 15glox + -15glox

Combine like terms: 15glox + -15glox = 0
-40glo + -11glox + 2glox2 = 0

Factor out the Greatest Common Factor (GCF), 'glo'.
glo(-40 + -11x + 2x2) = 0

Factor a trinomial.
glo((-5 + -2x)(8 + -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 '(-5 + -2x)' equal to zero and attempt to solve:

Simplifying
-5 + -2x = 0

Solving
-5 + -2x = 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 + -2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2x = 0 + 5
-2x = 0 + 5

Combine like terms: 0 + 5 = 5
-2x = 5

Add '2x' to each side of the equation.
-2x + 2x = 5 + 2x

Combine like terms: -2x + 2x = 0
0 = 5 + 2x

Simplifying
0 = 5 + 2x

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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