(u-1)(u-3)=48

Solution for (u-1)(u-3)=48 equation:

Simplifying
(u + -1)(u + -3) = 48

Reorder the terms:
(-1 + u)(u + -3) = 48

Reorder the terms:
(-1 + u)(-3 + u) = 48

Multiply (-1 + u) * (-3 + u)
(-1(-3 + u) + u(-3 + u)) = 48
((-3 * -1 + u * -1) + u(-3 + u)) = 48
((3 + -1u) + u(-3 + u)) = 48
(3 + -1u + (-3 * u + u * u)) = 48
(3 + -1u + (-3u + u2)) = 48

Combine like terms: -1u + -3u = -4u
(3 + -4u + u2) = 48

Solving
3 + -4u + u2 = 48

Solving for variable 'u'.

Reorder the terms:
3 + -48 + -4u + u2 = 48 + -48

Combine like terms: 3 + -48 = -45
-45 + -4u + u2 = 48 + -48

Combine like terms: 48 + -48 = 0
-45 + -4u + u2 = 0

Factor a trinomial.
(-5 + -1u)(9 + -1u) = 0

Subproblem 1
Set the factor '(-5 + -1u)' equal to zero and attempt to solve:

Simplifying
-5 + -1u = 0

Solving
-5 + -1u = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1u = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1u = 0 + 5
-1u = 0 + 5

Combine like terms: 0 + 5 = 5
-1u = 5

Divide each side by '-1'.
u = -5

Simplifying
u = -5
Subproblem 2
Set the factor '(9 + -1u)' equal to zero and attempt to solve:

Simplifying
9 + -1u = 0

Solving
9 + -1u = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1u = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1u = 0 + -9
-1u = 0 + -9

Combine like terms: 0 + -9 = -9
-1u = -9

Divide each side by '-1'.
u = 9

Simplifying
u = 9
Solution
u = {-5, 9}