log(a^2-6a)=log(10+3a)

Solution for log(a^2-6a)=log(10+3a) equation:

Simplifying
log(a2 + -6a) = log(10 + 3a)

Reorder the terms:
glo(-6a + a2) = log(10 + 3a)
(-6a * glo + a2 * glo) = log(10 + 3a)
(-6aglo + a2glo) = log(10 + 3a)
-6aglo + a2glo = (10 * glo + 3a * glo)

Reorder the terms:
-6aglo + a2glo = (3aglo + 10glo)
-6aglo + a2glo = (3aglo + 10glo)

Solving
-6aglo + a2glo = 3aglo + 10glo

Solving for variable 'a'.

Reorder the terms:
-6aglo + -3aglo + a2glo + -10glo = 3aglo + 10glo + -3aglo + -10glo

Combine like terms: -6aglo + -3aglo = -9aglo
-9aglo + a2glo + -10glo = 3aglo + 10glo + -3aglo + -10glo

Reorder the terms:
-9aglo + a2glo + -10glo = 3aglo + -3aglo + 10glo + -10glo

Combine like terms: 3aglo + -3aglo = 0
-9aglo + a2glo + -10glo = 0 + 10glo + -10glo
-9aglo + a2glo + -10glo = 10glo + -10glo

Combine like terms: 10glo + -10glo = 0
-9aglo + a2glo + -10glo = 0

Factor out the Greatest Common Factor (GCF), 'glo'.
glo(-9a + a2 + -10) = 0

Factor a trinomial.
glo((a + -10)(a + 1)) = 0

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

Simplifying
glo = 0

Solving
glo = 0

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

Add '-1glo' to each side of the equation.
glo + -1glo = 0 + -1glo
Remove the zero:
0 = -1glo

Simplifying
0 = -1glo

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 '(a + -10)' equal to zero and attempt to solve:

Simplifying
a + -10 = 0

Reorder the terms:
-10 + a = 0

Solving
-10 + a = 0

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

Add '10' to each side of the equation.
-10 + 10 + a = 0 + 10

Combine like terms: -10 + 10 = 0
0 + a = 0 + 10
a = 0 + 10

Combine like terms: 0 + 10 = 10
a = 10

Simplifying
a = 10
Subproblem 3
Set the factor '(a + 1)' equal to zero and attempt to solve:

Simplifying
a + 1 = 0

Reorder the terms:
1 + a = 0

Solving
1 + a = 0

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

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

Combine like terms: 1 + -1 = 0
0 + a = 0 + -1
a = 0 + -1

Combine like terms: 0 + -1 = -1
a = -1

Simplifying
a = -1
Solution
a = {10, -1}