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

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

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

Reorder the terms:
(-5 + 4a)(5a + 6) = 0

Reorder the terms:
(-5 + 4a)(6 + 5a) = 0

Multiply (-5 + 4a) * (6 + 5a)
(-5(6 + 5a) + 4a * (6 + 5a)) = 0
((6 * -5 + 5a * -5) + 4a * (6 + 5a)) = 0
((-30 + -25a) + 4a * (6 + 5a)) = 0
(-30 + -25a + (6 * 4a + 5a * 4a)) = 0
(-30 + -25a + (24a + 20a2)) = 0

Combine like terms: -25a + 24a = -1a
(-30 + -1a + 20a2) = 0

Solving
-30 + -1a + 20a2 = 0

Solving for variable 'a'.

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

Subproblem 1
Set the factor '(-6 + -5a)' equal to zero and attempt to solve:

Simplifying
-6 + -5a = 0

Solving
-6 + -5a = 0

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

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

Combine like terms: -6 + 6 = 0
0 + -5a = 0 + 6
-5a = 0 + 6

Combine like terms: 0 + 6 = 6
-5a = 6

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

Simplifying
a = -1.2
Subproblem 2
Set the factor '(5 + -4a)' equal to zero and attempt to solve:

Simplifying
5 + -4a = 0

Solving
5 + -4a = 0

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

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

Combine like terms: 5 + -5 = 0
0 + -4a = 0 + -5
-4a = 0 + -5

Combine like terms: 0 + -5 = -5
-4a = -5

Divide each side by '-4'.
a = 1.25

Simplifying
a = 1.25
Solution
a = {-1.2, 1.25}