(5a+1)(4a-1)=

Solution for (5a+1)(4a-1)= equation:

Simplifying
(5a + 1)(4a + -1) = 0

Reorder the terms:
(1 + 5a)(4a + -1) = 0

Reorder the terms:
(1 + 5a)(-1 + 4a) = 0

Multiply (1 + 5a) * (-1 + 4a)
(1(-1 + 4a) + 5a * (-1 + 4a)) = 0
((-1 * 1 + 4a * 1) + 5a * (-1 + 4a)) = 0
((-1 + 4a) + 5a * (-1 + 4a)) = 0
(-1 + 4a + (-1 * 5a + 4a * 5a)) = 0
(-1 + 4a + (-5a + 20a2)) = 0

Combine like terms: 4a + -5a = -1a
(-1 + -1a + 20a2) = 0

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

Solving for variable 'a'.

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

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

Simplifying
-1 + -5a = 0

Solving
-1 + -5a = 0

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

Add '1' to each side of the equation.
-1 + 1 + -5a = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -5a = 0 + 1
-5a = 0 + 1

Combine like terms: 0 + 1 = 1
-5a = 1

Divide each side by '-5'.
a = -0.2

Simplifying
a = -0.2
Subproblem 2
Set the factor '(1 + -4a)' equal to zero and attempt to solve:

Simplifying
1 + -4a = 0

Solving
1 + -4a = 0

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

Add '-1' to each side of the equation.
1 + -1 + -4a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4a = 0 + -1
-4a = 0 + -1

Combine like terms: 0 + -1 = -1
-4a = -1

Divide each side by '-4'.
a = 0.25

Simplifying
a = 0.25
Solution
a = {-0.2, 0.25}