(a-1)(a-4)=28

Solution for (a-1)(a-4)=28 equation:

Simplifying
(a + -1)(a + -4) = 28

Reorder the terms:
(-1 + a)(a + -4) = 28

Reorder the terms:
(-1 + a)(-4 + a) = 28

Multiply (-1 + a) * (-4 + a)
(-1(-4 + a) + a(-4 + a)) = 28
((-4 * -1 + a * -1) + a(-4 + a)) = 28
((4 + -1a) + a(-4 + a)) = 28
(4 + -1a + (-4 * a + a * a)) = 28
(4 + -1a + (-4a + a2)) = 28

Combine like terms: -1a + -4a = -5a
(4 + -5a + a2) = 28

Solving
4 + -5a + a2 = 28

Solving for variable 'a'.

Reorder the terms:
4 + -28 + -5a + a2 = 28 + -28

Combine like terms: 4 + -28 = -24
-24 + -5a + a2 = 28 + -28

Combine like terms: 28 + -28 = 0
-24 + -5a + a2 = 0

Factor a trinomial.
(-3 + -1a)(8 + -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 '(8 + -1a)' equal to zero and attempt to solve:

Simplifying
8 + -1a = 0

Solving
8 + -1a = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1a = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1a = 0 + -8
-1a = 0 + -8

Combine like terms: 0 + -8 = -8
-1a = -8

Divide each side by '-1'.
a = 8

Simplifying
a = 8
Solution
a = {-3, 8}