(2a-3b)(5a+6b)=

Solution for (2a-3b)(5a+6b)= equation:

Simplifying
(2a + -3b)(5a + 6b) = 0

Multiply (2a + -3b) * (5a + 6b)
(2a * (5a + 6b) + -3b * (5a + 6b)) = 0
((5a * 2a + 6b * 2a) + -3b * (5a + 6b)) = 0

Reorder the terms:
((12ab + 10a2) + -3b * (5a + 6b)) = 0
((12ab + 10a2) + -3b * (5a + 6b)) = 0
(12ab + 10a2 + (5a * -3b + 6b * -3b)) = 0
(12ab + 10a2 + (-15ab + -18b2)) = 0

Reorder the terms:
(12ab + -15ab + 10a2 + -18b2) = 0

Combine like terms: 12ab + -15ab = -3ab
(-3ab + 10a2 + -18b2) = 0

Solving
-3ab + 10a2 + -18b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(2a + -3b)(5a + 6b) = 0

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

Simplifying
2a + -3b = 0

Solving
2a + -3b = 0

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

Add '3b' to each side of the equation.
2a + -3b + 3b = 0 + 3b

Combine like terms: -3b + 3b = 0
2a + 0 = 0 + 3b
2a = 0 + 3b
Remove the zero:
2a = 3b

Divide each side by '2'.
a = 1.5b

Simplifying
a = 1.5b
Subproblem 2
Set the factor '(5a + 6b)' equal to zero and attempt to solve:

Simplifying
5a + 6b = 0

Solving
5a + 6b = 0

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

Add '-6b' to each side of the equation.
5a + 6b + -6b = 0 + -6b

Combine like terms: 6b + -6b = 0
5a + 0 = 0 + -6b
5a = 0 + -6b
Remove the zero:
5a = -6b

Divide each side by '5'.
a = -1.2b

Simplifying
a = -1.2b
Solution
a = {1.5b, -1.2b}