-(3a+2b)(5a-4b)=

Solution for -(3a+2b)(5a-4b)= equation:

Simplifying
-1(3a + 2b)(5a + -4b) = 0

Multiply (3a + 2b) * (5a + -4b)
-1(3a * (5a + -4b) + 2b * (5a + -4b)) = 0
-1((5a * 3a + -4b * 3a) + 2b * (5a + -4b)) = 0

Reorder the terms:
-1((-12ab + 15a2) + 2b * (5a + -4b)) = 0
-1((-12ab + 15a2) + 2b * (5a + -4b)) = 0
-1(-12ab + 15a2 + (5a * 2b + -4b * 2b)) = 0
-1(-12ab + 15a2 + (10ab + -8b2)) = 0

Reorder the terms:
-1(-12ab + 10ab + 15a2 + -8b2) = 0

Combine like terms: -12ab + 10ab = -2ab
-1(-2ab + 15a2 + -8b2) = 0
(-2ab * -1 + 15a2 * -1 + -8b2 * -1) = 0
(2ab + -15a2 + 8b2) = 0

Solving
2ab + -15a2 + 8b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-3a + -2b)(5a + -4b) = 0

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

Simplifying
-3a + -2b = 0

Solving
-3a + -2b = 0

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

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

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

Divide each side by '-3'.
a = -0.6666666667b

Simplifying
a = -0.6666666667b
Subproblem 2
Set the factor '(5a + -4b)' equal to zero and attempt to solve:

Simplifying
5a + -4b = 0

Solving
5a + -4b = 0

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

Add '4b' to each side of the equation.
5a + -4b + 4b = 0 + 4b

Combine like terms: -4b + 4b = 0
5a + 0 = 0 + 4b
5a = 0 + 4b
Remove the zero:
5a = 4b

Divide each side by '5'.
a = 0.8b

Simplifying
a = 0.8b
Solution
a = {-0.6666666667b, 0.8b}