(u-7)(u-1)=0

Solution for (u-7)(u-1)=0 equation:

Simplifying
(u + -7)(u + -1) = 0

Reorder the terms:
(-7 + u)(u + -1) = 0

Reorder the terms:
(-7 + u)(-1 + u) = 0

Multiply (-7 + u) * (-1 + u)
(-7(-1 + u) + u(-1 + u)) = 0
((-1 * -7 + u * -7) + u(-1 + u)) = 0
((7 + -7u) + u(-1 + u)) = 0
(7 + -7u + (-1 * u + u * u)) = 0
(7 + -7u + (-1u + u2)) = 0

Combine like terms: -7u + -1u = -8u
(7 + -8u + u2) = 0

Solving
7 + -8u + u2 = 0

Solving for variable 'u'.

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

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

Simplifying
1 + -1u = 0

Solving
1 + -1u = 0

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

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

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

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

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

Simplifying
u = 1
Subproblem 2
Set the factor '(7 + -1u)' equal to zero and attempt to solve:

Simplifying
7 + -1u = 0

Solving
7 + -1u = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1u = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1u = 0 + -7
-1u = 0 + -7

Combine like terms: 0 + -7 = -7
-1u = -7

Divide each side by '-1'.
u = 7

Simplifying
u = 7
Solution
u = {1, 7}