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

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


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

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

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

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

Combine like terms: -2u + -3u = -5u
(6 + -5u + u2) = (u + 2)(u + -4) + (u + 2)(u + -2)

Reorder the terms:
6 + -5u + u2 = (2 + u)(u + -4) + (u + 2)(u + -2)

Reorder the terms:
6 + -5u + u2 = (2 + u)(-4 + u) + (u + 2)(u + -2)

Multiply (2 + u) * (-4 + u)
6 + -5u + u2 = (2(-4 + u) + u(-4 + u)) + (u + 2)(u + -2)
6 + -5u + u2 = ((-4 * 2 + u * 2) + u(-4 + u)) + (u + 2)(u + -2)
6 + -5u + u2 = ((-8 + 2u) + u(-4 + u)) + (u + 2)(u + -2)
6 + -5u + u2 = (-8 + 2u + (-4 * u + u * u)) + (u + 2)(u + -2)
6 + -5u + u2 = (-8 + 2u + (-4u + u2)) + (u + 2)(u + -2)

Combine like terms: 2u + -4u = -2u
6 + -5u + u2 = (-8 + -2u + u2) + (u + 2)(u + -2)

Reorder the terms:
6 + -5u + u2 = -8 + -2u + u2 + (2 + u)(u + -2)

Reorder the terms:
6 + -5u + u2 = -8 + -2u + u2 + (2 + u)(-2 + u)

Multiply (2 + u) * (-2 + u)
6 + -5u + u2 = -8 + -2u + u2 + (2(-2 + u) + u(-2 + u))
6 + -5u + u2 = -8 + -2u + u2 + ((-2 * 2 + u * 2) + u(-2 + u))
6 + -5u + u2 = -8 + -2u + u2 + ((-4 + 2u) + u(-2 + u))
6 + -5u + u2 = -8 + -2u + u2 + (-4 + 2u + (-2 * u + u * u))
6 + -5u + u2 = -8 + -2u + u2 + (-4 + 2u + (-2u + u2))

Combine like terms: 2u + -2u = 0
6 + -5u + u2 = -8 + -2u + u2 + (-4 + 0 + u2)
6 + -5u + u2 = -8 + -2u + u2 + (-4 + u2)

Reorder the terms:
6 + -5u + u2 = -8 + -4 + -2u + u2 + u2

Combine like terms: -8 + -4 = -12
6 + -5u + u2 = -12 + -2u + u2 + u2

Combine like terms: u2 + u2 = 2u2
6 + -5u + u2 = -12 + -2u + 2u2

Solving
6 + -5u + u2 = -12 + -2u + 2u2

Solving for variable 'u'.

Reorder the terms:
6 + 12 + -5u + 2u + u2 + -2u2 = -12 + -2u + 2u2 + 12 + 2u + -2u2

Combine like terms: 6 + 12 = 18
18 + -5u + 2u + u2 + -2u2 = -12 + -2u + 2u2 + 12 + 2u + -2u2

Combine like terms: -5u + 2u = -3u
18 + -3u + u2 + -2u2 = -12 + -2u + 2u2 + 12 + 2u + -2u2

Combine like terms: u2 + -2u2 = -1u2
18 + -3u + -1u2 = -12 + -2u + 2u2 + 12 + 2u + -2u2

Reorder the terms:
18 + -3u + -1u2 = -12 + 12 + -2u + 2u + 2u2 + -2u2

Combine like terms: -12 + 12 = 0
18 + -3u + -1u2 = 0 + -2u + 2u + 2u2 + -2u2
18 + -3u + -1u2 = -2u + 2u + 2u2 + -2u2

Combine like terms: -2u + 2u = 0
18 + -3u + -1u2 = 0 + 2u2 + -2u2
18 + -3u + -1u2 = 2u2 + -2u2

Combine like terms: 2u2 + -2u2 = 0
18 + -3u + -1u2 = 0

Factor a trinomial.
(3 + -1u)(6 + u) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(6 + u)' equal to zero and attempt to solve:

Simplifying
6 + u = 0

Solving
6 + u = 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 + u = 0 + -6

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

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

Simplifying
u = -6
Solution
u = {3, -6}

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