(u+3)(u-4)=18

Solution for (u+3)(u-4)=18 equation:

Simplifying
(u + 3)(u + -4) = 18

Reorder the terms:
(3 + u)(u + -4) = 18

Reorder the terms:
(3 + u)(-4 + u) = 18

Multiply (3 + u) * (-4 + u)
(3(-4 + u) + u(-4 + u)) = 18
((-4 * 3 + u * 3) + u(-4 + u)) = 18
((-12 + 3u) + u(-4 + u)) = 18
(-12 + 3u + (-4 * u + u * u)) = 18
(-12 + 3u + (-4u + u2)) = 18

Combine like terms: 3u + -4u = -1u
(-12 + -1u + u2) = 18

Solving
-12 + -1u + u2 = 18

Solving for variable 'u'.

Reorder the terms:
-12 + -18 + -1u + u2 = 18 + -18

Combine like terms: -12 + -18 = -30
-30 + -1u + u2 = 18 + -18

Combine like terms: 18 + -18 = 0
-30 + -1u + u2 = 0

Factor a trinomial.
(-5 + -1u)(6 + -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 '(6 + -1u)' equal to zero and attempt to solve:

Simplifying
6 + -1u = 0

Solving
6 + -1u = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1u = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1u = 0 + -6
-1u = 0 + -6

Combine like terms: 0 + -6 = -6
-1u = -6

Divide each side by '-1'.
u = 6

Simplifying
u = 6
Solution
u = {-5, 6}