(u-7)(u+5)=0

Solution for (u-7)(u+5)=0 equation:

Simplifying
(u + -7)(u + 5) = 0

Reorder the terms:
(-7 + u)(u + 5) = 0

Reorder the terms:
(-7 + u)(5 + u) = 0

Multiply (-7 + u) * (5 + u)
(-7(5 + u) + u(5 + u)) = 0
((5 * -7 + u * -7) + u(5 + u)) = 0
((-35 + -7u) + u(5 + u)) = 0
(-35 + -7u + (5 * u + u * u)) = 0
(-35 + -7u + (5u + u2)) = 0

Combine like terms: -7u + 5u = -2u
(-35 + -2u + u2) = 0

Solving
-35 + -2u + u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-5 + -1u)(7 + -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 '(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 = {-5, 7}