(4a-1)(a-3a+1)=

Solution for (4a-1)(a-3a+1)= equation:

Simplifying
(4a + -1)(a + -3a + 1) = 0

Reorder the terms:
(-1 + 4a)(a + -3a + 1) = 0

Reorder the terms:
(-1 + 4a)(1 + a + -3a) = 0

Combine like terms: a + -3a = -2a
(-1 + 4a)(1 + -2a) = 0

Multiply (-1 + 4a) * (1 + -2a)
(-1(1 + -2a) + 4a * (1 + -2a)) = 0
((1 * -1 + -2a * -1) + 4a * (1 + -2a)) = 0
((-1 + 2a) + 4a * (1 + -2a)) = 0
(-1 + 2a + (1 * 4a + -2a * 4a)) = 0
(-1 + 2a + (4a + -8a2)) = 0

Combine like terms: 2a + 4a = 6a
(-1 + 6a + -8a2) = 0

Solving
-1 + 6a + -8a2 = 0

Solving for variable 'a'.

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

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

Simplifying
-1 + 2a = 0

Solving
-1 + 2a = 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 + 2a = 0 + 1

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

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

Divide each side by '2'.
a = 0.5

Simplifying
a = 0.5
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 = {0.5, 0.25}