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

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

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

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

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

Multiply (4 + 5a) * (-5 + 4a)
(4(-5 + 4a) + 5a * (-5 + 4a)) = 0
((-5 * 4 + 4a * 4) + 5a * (-5 + 4a)) = 0
((-20 + 16a) + 5a * (-5 + 4a)) = 0
(-20 + 16a + (-5 * 5a + 4a * 5a)) = 0
(-20 + 16a + (-25a + 20a2)) = 0

Combine like terms: 16a + -25a = -9a
(-20 + -9a + 20a2) = 0

Solving
-20 + -9a + 20a2 = 0

Solving for variable 'a'.

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

Subproblem 1
Set the factor '(-4 + -5a)' equal to zero and attempt to solve:

Simplifying
-4 + -5a = 0

Solving
-4 + -5a = 0

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

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

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

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

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

Simplifying
a = -0.8
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 = {-0.8, 1.25}