(4a+3b)(5a-6b)=

Solution for (4a+3b)(5a-6b)= equation:

Simplifying
(4a + 3b)(5a + -6b) = 0

Multiply (4a + 3b) * (5a + -6b)
(4a * (5a + -6b) + 3b * (5a + -6b)) = 0
((5a * 4a + -6b * 4a) + 3b * (5a + -6b)) = 0

Reorder the terms:
((-24ab + 20a2) + 3b * (5a + -6b)) = 0
((-24ab + 20a2) + 3b * (5a + -6b)) = 0
(-24ab + 20a2 + (5a * 3b + -6b * 3b)) = 0
(-24ab + 20a2 + (15ab + -18b2)) = 0

Reorder the terms:
(-24ab + 15ab + 20a2 + -18b2) = 0

Combine like terms: -24ab + 15ab = -9ab
(-9ab + 20a2 + -18b2) = 0

Solving
-9ab + 20a2 + -18b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(5a + -6b)(4a + 3b) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(4a + 3b)' equal to zero and attempt to solve:

Simplifying
4a + 3b = 0

Solving
4a + 3b = 0

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

Add '-3b' to each side of the equation.
4a + 3b + -3b = 0 + -3b

Combine like terms: 3b + -3b = 0
4a + 0 = 0 + -3b
4a = 0 + -3b
Remove the zero:
4a = -3b

Divide each side by '4'.
a = -0.75b

Simplifying
a = -0.75b
Solution
a = {1.2b, -0.75b}