a(a-2b)-6a(a+b)=

Solution for a(a-2b)-6a(a+b)= equation:

Simplifying
a(a + -2b) + -6a(a + b) = 0
(a * a + -2b * a) + -6a(a + b) = 0

Reorder the terms:
(-2ab + a2) + -6a(a + b) = 0
(-2ab + a2) + -6a(a + b) = 0
-2ab + a2 + (a * -6a + b * -6a) = 0

Reorder the terms:
-2ab + a2 + (-6ab + -6a2) = 0
-2ab + a2 + (-6ab + -6a2) = 0

Reorder the terms:
-2ab + -6ab + a2 + -6a2 = 0

Combine like terms: -2ab + -6ab = -8ab
-8ab + a2 + -6a2 = 0

Combine like terms: a2 + -6a2 = -5a2
-8ab + -5a2 = 0

Solving
-8ab + -5a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '-1a'.
-1a(8b + 5a) = 0

Ignore the factor -1.
Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0
Subproblem 2
Set the factor '(8b + 5a)' equal to zero and attempt to solve:

Simplifying
8b + 5a = 0

Reorder the terms:
5a + 8b = 0

Solving
5a + 8b = 0

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

Add '-8b' to each side of the equation.
5a + 8b + -8b = 0 + -8b

Combine like terms: 8b + -8b = 0
5a + 0 = 0 + -8b
5a = 0 + -8b
Remove the zero:
5a = -8b

Divide each side by '5'.
a = -1.6b

Simplifying
a = -1.6b
Solution
a = {0, -1.6b}