u^2-2u+32=(2u-5)(u+2)

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Solution for u^2-2u+32=(2u-5)(u+2) equation: 


Simplifying
u2 + -2u + 32 = (2u + -5)(u + 2)

Reorder the terms:
32 + -2u + u2 = (2u + -5)(u + 2)

Reorder the terms:
32 + -2u + u2 = (-5 + 2u)(u + 2)

Reorder the terms:
32 + -2u + u2 = (-5 + 2u)(2 + u)

Multiply (-5 + 2u) * (2 + u)
32 + -2u + u2 = (-5(2 + u) + 2u * (2 + u))
32 + -2u + u2 = ((2 * -5 + u * -5) + 2u * (2 + u))
32 + -2u + u2 = ((-10 + -5u) + 2u * (2 + u))
32 + -2u + u2 = (-10 + -5u + (2 * 2u + u * 2u))
32 + -2u + u2 = (-10 + -5u + (4u + 2u2))

Combine like terms: -5u + 4u = -1u
32 + -2u + u2 = (-10 + -1u + 2u2)

Solving
32 + -2u + u2 = -10 + -1u + 2u2

Solving for variable 'u'.

Reorder the terms:
32 + 10 + -2u + u + u2 + -2u2 = -10 + -1u + 2u2 + 10 + u + -2u2

Combine like terms: 32 + 10 = 42
42 + -2u + u + u2 + -2u2 = -10 + -1u + 2u2 + 10 + u + -2u2

Combine like terms: -2u + u = -1u
42 + -1u + u2 + -2u2 = -10 + -1u + 2u2 + 10 + u + -2u2

Combine like terms: u2 + -2u2 = -1u2
42 + -1u + -1u2 = -10 + -1u + 2u2 + 10 + u + -2u2

Reorder the terms:
42 + -1u + -1u2 = -10 + 10 + -1u + u + 2u2 + -2u2

Combine like terms: -10 + 10 = 0
42 + -1u + -1u2 = 0 + -1u + u + 2u2 + -2u2
42 + -1u + -1u2 = -1u + u + 2u2 + -2u2

Combine like terms: -1u + u = 0
42 + -1u + -1u2 = 0 + 2u2 + -2u2
42 + -1u + -1u2 = 2u2 + -2u2

Combine like terms: 2u2 + -2u2 = 0
42 + -1u + -1u2 = 0

Factor a trinomial.
(6 + -1u)(7 + u) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(7 + u)' equal to zero and attempt to solve:

Simplifying
7 + u = 0

Solving
7 + u = 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 + u = 0 + -7

Combine like terms: 7 + -7 = 0
0 + u = 0 + -7
u = 0 + -7

Combine like terms: 0 + -7 = -7
u = -7

Simplifying
u = -7
Solution
u = {6, -7}

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