(4a-1)(a+9)=0

Solution for (4a-1)(a+9)=0 equation:

Simplifying
(4a + -1)(a + 9) = 0

Reorder the terms:
(-1 + 4a)(a + 9) = 0

Reorder the terms:
(-1 + 4a)(9 + a) = 0

Multiply (-1 + 4a) * (9 + a)
(-1(9 + a) + 4a * (9 + a)) = 0
((9 * -1 + a * -1) + 4a * (9 + a)) = 0
((-9 + -1a) + 4a * (9 + a)) = 0
(-9 + -1a + (9 * 4a + a * 4a)) = 0
(-9 + -1a + (36a + 4a2)) = 0

Combine like terms: -1a + 36a = 35a
(-9 + 35a + 4a2) = 0

Solving
-9 + 35a + 4a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-9 + -1a)(1 + -4a) = 0

Subproblem 1
Set the factor '(-9 + -1a)' equal to zero and attempt to solve:

Simplifying
-9 + -1a = 0

Solving
-9 + -1a = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1a = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1a = 0 + 9
-1a = 0 + 9

Combine like terms: 0 + 9 = 9
-1a = 9

Divide each side by '-1'.
a = -9

Simplifying
a = -9
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 = {-9, 0.25}