(2a-1)(a-1)=6

Solution for (2a-1)(a-1)=6 equation:

Simplifying
(2a + -1)(a + -1) = 6

Reorder the terms:
(-1 + 2a)(a + -1) = 6

Reorder the terms:
(-1 + 2a)(-1 + a) = 6

Multiply (-1 + 2a) * (-1 + a)
(-1(-1 + a) + 2a * (-1 + a)) = 6
((-1 * -1 + a * -1) + 2a * (-1 + a)) = 6
((1 + -1a) + 2a * (-1 + a)) = 6
(1 + -1a + (-1 * 2a + a * 2a)) = 6
(1 + -1a + (-2a + 2a2)) = 6

Combine like terms: -1a + -2a = -3a
(1 + -3a + 2a2) = 6

Solving
1 + -3a + 2a2 = 6

Solving for variable 'a'.

Reorder the terms:
1 + -6 + -3a + 2a2 = 6 + -6

Combine like terms: 1 + -6 = -5
-5 + -3a + 2a2 = 6 + -6

Combine like terms: 6 + -6 = 0
-5 + -3a + 2a2 = 0

Factor a trinomial.
(-1 + -1a)(5 + -2a) = 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 '(5 + -2a)' equal to zero and attempt to solve:

Simplifying
5 + -2a = 0

Solving
5 + -2a = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2a = 0 + -5
-2a = 0 + -5

Combine like terms: 0 + -5 = -5
-2a = -5

Divide each side by '-2'.
a = 2.5

Simplifying
a = 2.5
Solution
a = {-1, 2.5}