(a-1)(a-1)-5(a-1)=-6

Solution for (a-1)(a-1)-5(a-1)=-6 equation:

Simplifying
(a + -1)(a + -1) + -5(a + -1) = -6

Reorder the terms:
(-1 + a)(a + -1) + -5(a + -1) = -6

Reorder the terms:
(-1 + a)(-1 + a) + -5(a + -1) = -6

Multiply (-1 + a) * (-1 + a)
(-1(-1 + a) + a(-1 + a)) + -5(a + -1) = -6
((-1 * -1 + a * -1) + a(-1 + a)) + -5(a + -1) = -6
((1 + -1a) + a(-1 + a)) + -5(a + -1) = -6
(1 + -1a + (-1 * a + a * a)) + -5(a + -1) = -6
(1 + -1a + (-1a + a2)) + -5(a + -1) = -6

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

Reorder the terms:
1 + -2a + a2 + -5(-1 + a) = -6
1 + -2a + a2 + (-1 * -5 + a * -5) = -6
1 + -2a + a2 + (5 + -5a) = -6

Reorder the terms:
1 + 5 + -2a + -5a + a2 = -6

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

Combine like terms: -2a + -5a = -7a
6 + -7a + a2 = -6

Solving
6 + -7a + a2 = -6

Solving for variable 'a'.

Reorder the terms:
6 + 6 + -7a + a2 = -6 + 6

Combine like terms: 6 + 6 = 12
12 + -7a + a2 = -6 + 6

Combine like terms: -6 + 6 = 0
12 + -7a + a2 = 0

Factor a trinomial.
(3 + -1a)(4 + -1a) = 0

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

Simplifying
3 + -1a = 0

Solving
3 + -1a = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1a = 0 + -3
-1a = 0 + -3

Combine like terms: 0 + -3 = -3
-1a = -3

Divide each side by '-1'.
a = 3

Simplifying
a = 3
Subproblem 2
Set the factor '(4 + -1a)' equal to zero and attempt to solve:

Simplifying
4 + -1a = 0

Solving
4 + -1a = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1a = 0 + -4
-1a = 0 + -4

Combine like terms: 0 + -4 = -4
-1a = -4

Divide each side by '-1'.
a = 4

Simplifying
a = 4
Solution
a = {3, 4}