(15a-3b)*(7a+6b)=

Solution for (15a-3b)*(7a+6b)= equation:

Simplifying
(15a + -3b)(7a + 6b) = 0

Multiply (15a + -3b) * (7a + 6b)
(15a * (7a + 6b) + -3b * (7a + 6b)) = 0
((7a * 15a + 6b * 15a) + -3b * (7a + 6b)) = 0

Reorder the terms:
((90ab + 105a2) + -3b * (7a + 6b)) = 0
((90ab + 105a2) + -3b * (7a + 6b)) = 0
(90ab + 105a2 + (7a * -3b + 6b * -3b)) = 0
(90ab + 105a2 + (-21ab + -18b2)) = 0

Reorder the terms:
(90ab + -21ab + 105a2 + -18b2) = 0

Combine like terms: 90ab + -21ab = 69ab
(69ab + 105a2 + -18b2) = 0

Solving
69ab + 105a2 + -18b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(23ab + 35a2 + -6b2) = 0

Factor a trinomial.
3((5a + -1b)(7a + 6b)) = 0

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
Set the factor '(7a + 6b)' equal to zero and attempt to solve:

Simplifying
7a + 6b = 0

Solving
7a + 6b = 0

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

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

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

Divide each side by '7'.
a = -0.8571428571b

Simplifying
a = -0.8571428571b
Solution
a = {0.2b, -0.8571428571b}