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

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

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

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

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

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

Combine like terms: 1a + -4a = -3a
(-1 + -3a + 4a2) = 0

Solving
-1 + -3a + 4a2 = 0

Solving for variable 'a'.

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

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

Simplifying
1 + -1a = 0

Solving
1 + -1a = 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 + -1a = 0 + -1

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

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

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

Simplifying
a = 1
Solution
a = {-0.25, 1}