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

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


Simplifying
log2(a2 + -6a) = log2(10 + 3a)

Reorder the terms:
g2lo(-6a + a2) = log2(10 + 3a)
(-6a * g2lo + a2 * g2lo) = log2(10 + 3a)
(-6ag2lo + a2g2lo) = log2(10 + 3a)
-6ag2lo + a2g2lo = (10 * g2lo + 3a * g2lo)

Reorder the terms:
-6ag2lo + a2g2lo = (3ag2lo + 10g2lo)
-6ag2lo + a2g2lo = (3ag2lo + 10g2lo)

Solving
-6ag2lo + a2g2lo = 3ag2lo + 10g2lo

Solving for variable 'a'.

Reorder the terms:
-6ag2lo + -3ag2lo + a2g2lo + -10g2lo = 3ag2lo + 10g2lo + -3ag2lo + -10g2lo

Combine like terms: -6ag2lo + -3ag2lo = -9ag2lo
-9ag2lo + a2g2lo + -10g2lo = 3ag2lo + 10g2lo + -3ag2lo + -10g2lo

Reorder the terms:
-9ag2lo + a2g2lo + -10g2lo = 3ag2lo + -3ag2lo + 10g2lo + -10g2lo

Combine like terms: 3ag2lo + -3ag2lo = 0
-9ag2lo + a2g2lo + -10g2lo = 0 + 10g2lo + -10g2lo
-9ag2lo + a2g2lo + -10g2lo = 10g2lo + -10g2lo

Combine like terms: 10g2lo + -10g2lo = 0
-9ag2lo + a2g2lo + -10g2lo = 0

Factor out the Greatest Common Factor (GCF), 'g2lo'.
g2lo(-9a + a2 + -10) = 0

Factor a trinomial.
g2lo((a + -10)(a + 1)) = 0


Subproblem 1
Set the factor 'g2lo' equal to zero and attempt to solve:

Simplifying
g2lo = 0

Solving
g2lo = 0

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

Add '-1g2lo' to each side of the equation.
g2lo + -1g2lo = 0 + -1g2lo
Remove the zero:
0 = -1g2lo

Simplifying
0 = -1g2lo

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}

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