=(u-2)(u+3)

Solution for =(u-2)(u+3) equation:

Simplifying
0 = (u + -2)(u + 3)

Reorder the terms:
0 = (-2 + u)(u + 3)

Reorder the terms:
0 = (-2 + u)(3 + u)

Multiply (-2 + u) * (3 + u)
0 = (-2(3 + u) + u(3 + u))
0 = ((3 * -2 + u * -2) + u(3 + u))
0 = ((-6 + -2u) + u(3 + u))
0 = (-6 + -2u + (3 * u + u * u))
0 = (-6 + -2u + (3u + u2))

Combine like terms: -2u + 3u = 1u
0 = (-6 + 1u + u2)

Solving
0 = -6 + 1u + u2

Solving for variable 'u'.

Combine like terms: 0 + 6 = 6
6 + -1u + -1u2 = -6 + 1u + u2 + 6 + -1u + -1u2

Reorder the terms:
6 + -1u + -1u2 = -6 + 6 + 1u + -1u + u2 + -1u2

Combine like terms: -6 + 6 = 0
6 + -1u + -1u2 = 0 + 1u + -1u + u2 + -1u2
6 + -1u + -1u2 = 1u + -1u + u2 + -1u2

Combine like terms: 1u + -1u = 0
6 + -1u + -1u2 = 0 + u2 + -1u2
6 + -1u + -1u2 = u2 + -1u2

Combine like terms: u2 + -1u2 = 0
6 + -1u + -1u2 = 0

Factor a trinomial.
(2 + -1u)(3 + u) = 0

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

Simplifying
2 + -1u = 0

Solving
2 + -1u = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1u = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1u = 0 + -2
-1u = 0 + -2

Combine like terms: 0 + -2 = -2
-1u = -2

Divide each side by '-1'.
u = 2

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

Simplifying
3 + u = 0

Solving
3 + u = 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 + u = 0 + -3

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

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

Simplifying
u = -3
Solution
u = {2, -3}