(3a-1)(a-1)=8

Solution for (3a-1)(a-1)=8 equation:

Simplifying
(3a + -1)(a + -1) = 8

Reorder the terms:
(-1 + 3a)(a + -1) = 8

Reorder the terms:
(-1 + 3a)(-1 + a) = 8

Multiply (-1 + 3a) * (-1 + a)
(-1(-1 + a) + 3a * (-1 + a)) = 8
((-1 * -1 + a * -1) + 3a * (-1 + a)) = 8
((1 + -1a) + 3a * (-1 + a)) = 8
(1 + -1a + (-1 * 3a + a * 3a)) = 8
(1 + -1a + (-3a + 3a2)) = 8

Combine like terms: -1a + -3a = -4a
(1 + -4a + 3a2) = 8

Solving
1 + -4a + 3a2 = 8

Solving for variable 'a'.

Reorder the terms:
1 + -8 + -4a + 3a2 = 8 + -8

Combine like terms: 1 + -8 = -7
-7 + -4a + 3a2 = 8 + -8

Combine like terms: 8 + -8 = 0
-7 + -4a + 3a2 = 0

Factor a trinomial.
(-1 + -1a)(7 + -3a) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(7 + -3a)' equal to zero and attempt to solve:

Simplifying
7 + -3a = 0

Solving
7 + -3a = 0

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

Add '-7' to each side of the equation.
7 + -7 + -3a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3a = 0 + -7
-3a = 0 + -7

Combine like terms: 0 + -7 = -7
-3a = -7

Divide each side by '-3'.
a = 2.333333333

Simplifying
a = 2.333333333
Solution
a = {-1, 2.333333333}