(u-3)(u+7)=

Solution for (u-3)(u+7)= equation:

Simplifying
(u + -3)(u + 7) = 0

Reorder the terms:
(-3 + u)(u + 7) = 0

Reorder the terms:
(-3 + u)(7 + u) = 0

Multiply (-3 + u) * (7 + u)
(-3(7 + u) + u(7 + u)) = 0
((7 * -3 + u * -3) + u(7 + u)) = 0
((-21 + -3u) + u(7 + u)) = 0
(-21 + -3u + (7 * u + u * u)) = 0
(-21 + -3u + (7u + u2)) = 0

Combine like terms: -3u + 7u = 4u
(-21 + 4u + u2) = 0

Solving
-21 + 4u + u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-7 + -1u)(3 + -1u) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(3 + -1u)' equal to zero and attempt to solve:

Simplifying
3 + -1u = 0

Solving
3 + -1u = 0

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

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

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

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

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

Simplifying
u = 3
Solution
u = {-7, 3}