(6a-2b)(9a+b)=

Solution for (6a-2b)(9a+b)= equation:

Simplifying
(6a + -2b)(9a + b) = 0

Multiply (6a + -2b) * (9a + b)
(6a * (9a + b) + -2b * (9a + b)) = 0
((9a * 6a + b * 6a) + -2b * (9a + b)) = 0

Reorder the terms:
((6ab + 54a2) + -2b * (9a + b)) = 0
((6ab + 54a2) + -2b * (9a + b)) = 0
(6ab + 54a2 + (9a * -2b + b * -2b)) = 0
(6ab + 54a2 + (-18ab + -2b2)) = 0

Reorder the terms:
(6ab + -18ab + 54a2 + -2b2) = 0

Combine like terms: 6ab + -18ab = -12ab
(-12ab + 54a2 + -2b2) = 0

Solving
-12ab + 54a2 + -2b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6ab + 27a2 + -1b2) = 0

Factor a trinomial.
2((3a + -1b)(9a + b)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3a + -1b)' equal to zero and attempt to solve:

Simplifying
3a + -1b = 0

Solving
3a + -1b = 0

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

Add 'b' to each side of the equation.
3a + -1b + b = 0 + b

Combine like terms: -1b + b = 0
3a + 0 = 0 + b
3a = 0 + b
Remove the zero:
3a = b

Divide each side by '3'.
a = 0.3333333333b

Simplifying
a = 0.3333333333b
Subproblem 2
Set the factor '(9a + b)' equal to zero and attempt to solve:

Simplifying
9a + b = 0

Solving
9a + b = 0

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

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

Combine like terms: b + -1b = 0
9a + 0 = 0 + -1b
9a = 0 + -1b
Remove the zero:
9a = -1b

Divide each side by '9'.
a = -0.1111111111b

Simplifying
a = -0.1111111111b
Solution
a = {0.3333333333b, -0.1111111111b}