(5a-b)(6a-7b)=

Solution for (5a-b)(6a-7b)= equation:

Simplifying
(5a + -1b)(6a + -7b) = 0

Multiply (5a + -1b) * (6a + -7b)
(5a * (6a + -7b) + -1b * (6a + -7b)) = 0
((6a * 5a + -7b * 5a) + -1b * (6a + -7b)) = 0

Reorder the terms:
((-35ab + 30a2) + -1b * (6a + -7b)) = 0
((-35ab + 30a2) + -1b * (6a + -7b)) = 0
(-35ab + 30a2 + (6a * -1b + -7b * -1b)) = 0
(-35ab + 30a2 + (-6ab + 7b2)) = 0

Reorder the terms:
(-35ab + -6ab + 30a2 + 7b2) = 0

Combine like terms: -35ab + -6ab = -41ab
(-41ab + 30a2 + 7b2) = 0

Solving
-41ab + 30a2 + 7b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(6a + -7b)(5a + -1b) = 0

Subproblem 1
Set the factor '(6a + -7b)' equal to zero and attempt to solve:

Simplifying
6a + -7b = 0

Solving
6a + -7b = 0

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

Add '7b' to each side of the equation.
6a + -7b + 7b = 0 + 7b

Combine like terms: -7b + 7b = 0
6a + 0 = 0 + 7b
6a = 0 + 7b
Remove the zero:
6a = 7b

Divide each side by '6'.
a = 1.166666667b

Simplifying
a = 1.166666667b
Subproblem 2
Set the factor '(5a + -1b)' equal to zero and attempt to solve:

Simplifying
5a + -1b = 0

Solving
5a + -1b = 0

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

Add 'b' to each side of the equation.
5a + -1b + b = 0 + b

Combine like terms: -1b + b = 0
5a + 0 = 0 + b
5a = 0 + b
Remove the zero:
5a = b

Divide each side by '5'.
a = 0.2b

Simplifying
a = 0.2b
Solution
a = {1.166666667b, 0.2b}