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

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

Simplifying
(2a + -4)(4a + 5) = 0

Reorder the terms:
(-4 + 2a)(4a + 5) = 0

Reorder the terms:
(-4 + 2a)(5 + 4a) = 0

Multiply (-4 + 2a) * (5 + 4a)
(-4(5 + 4a) + 2a * (5 + 4a)) = 0
((5 * -4 + 4a * -4) + 2a * (5 + 4a)) = 0
((-20 + -16a) + 2a * (5 + 4a)) = 0
(-20 + -16a + (5 * 2a + 4a * 2a)) = 0
(-20 + -16a + (10a + 8a2)) = 0

Combine like terms: -16a + 10a = -6a
(-20 + -6a + 8a2) = 0

Solving
-20 + -6a + 8a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + -3a + 4a2) = 0

Factor a trinomial.
2((-5 + -4a)(2 + -1a)) = 0

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

Simplifying
2 + -1a = 0

Solving
2 + -1a = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1a = 0 + -2
-1a = 0 + -2

Combine like terms: 0 + -2 = -2
-1a = -2

Divide each side by '-1'.
a = 2

Simplifying
a = 2
Solution
a = {-1.25, 2}