u^2-2u+4=(2u-3)(u+2)

Solution for u^2-2u+4=(2u-3)(u+2) equation:

Simplifying
u2 + -2u + 4 = (2u + -3)(u + 2)

Reorder the terms:
4 + -2u + u2 = (2u + -3)(u + 2)

Reorder the terms:
4 + -2u + u2 = (-3 + 2u)(u + 2)

Reorder the terms:
4 + -2u + u2 = (-3 + 2u)(2 + u)

Multiply (-3 + 2u) * (2 + u)
4 + -2u + u2 = (-3(2 + u) + 2u * (2 + u))
4 + -2u + u2 = ((2 * -3 + u * -3) + 2u * (2 + u))
4 + -2u + u2 = ((-6 + -3u) + 2u * (2 + u))
4 + -2u + u2 = (-6 + -3u + (2 * 2u + u * 2u))
4 + -2u + u2 = (-6 + -3u + (4u + 2u2))

Combine like terms: -3u + 4u = 1u
4 + -2u + u2 = (-6 + 1u + 2u2)

Solving
4 + -2u + u2 = -6 + 1u + 2u2

Solving for variable 'u'.

Reorder the terms:
4 + 6 + -2u + -1u + u2 + -2u2 = -6 + 1u + 2u2 + 6 + -1u + -2u2

Combine like terms: 4 + 6 = 10
10 + -2u + -1u + u2 + -2u2 = -6 + 1u + 2u2 + 6 + -1u + -2u2

Combine like terms: -2u + -1u = -3u
10 + -3u + u2 + -2u2 = -6 + 1u + 2u2 + 6 + -1u + -2u2

Combine like terms: u2 + -2u2 = -1u2
10 + -3u + -1u2 = -6 + 1u + 2u2 + 6 + -1u + -2u2

Reorder the terms:
10 + -3u + -1u2 = -6 + 6 + 1u + -1u + 2u2 + -2u2

Combine like terms: -6 + 6 = 0
10 + -3u + -1u2 = 0 + 1u + -1u + 2u2 + -2u2
10 + -3u + -1u2 = 1u + -1u + 2u2 + -2u2

Combine like terms: 1u + -1u = 0
10 + -3u + -1u2 = 0 + 2u2 + -2u2
10 + -3u + -1u2 = 2u2 + -2u2

Combine like terms: 2u2 + -2u2 = 0
10 + -3u + -1u2 = 0

Factor a trinomial.
(2 + -1u)(5 + 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 '(5 + u)' equal to zero and attempt to solve:

Simplifying
5 + u = 0

Solving
5 + u = 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 + u = 0 + -5

Combine like terms: 5 + -5 = 0
0 + u = 0 + -5
u = 0 + -5

Combine like terms: 0 + -5 = -5
u = -5

Simplifying
u = -5
Solution
u = {2, -5}