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

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

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

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

Reorder the terms:
((-15ab + 20a2) + 6b * (4a + -3b)) = 0
((-15ab + 20a2) + 6b * (4a + -3b)) = 0
(-15ab + 20a2 + (4a * 6b + -3b * 6b)) = 0
(-15ab + 20a2 + (24ab + -18b2)) = 0

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

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

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

Solving for variable 'a'.

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

Subproblem 1
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
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 = {0.75b, -1.2b}