2u^2-11u+14=(u-2)(u-2)

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Solution for 2u^2-11u+14=(u-2)(u-2) equation: 


Simplifying
2u2 + -11u + 14 = (u + -2)(u + -2)

Reorder the terms:
14 + -11u + 2u2 = (u + -2)(u + -2)

Reorder the terms:
14 + -11u + 2u2 = (-2 + u)(u + -2)

Reorder the terms:
14 + -11u + 2u2 = (-2 + u)(-2 + u)

Multiply (-2 + u) * (-2 + u)
14 + -11u + 2u2 = (-2(-2 + u) + u(-2 + u))
14 + -11u + 2u2 = ((-2 * -2 + u * -2) + u(-2 + u))
14 + -11u + 2u2 = ((4 + -2u) + u(-2 + u))
14 + -11u + 2u2 = (4 + -2u + (-2 * u + u * u))
14 + -11u + 2u2 = (4 + -2u + (-2u + u2))

Combine like terms: -2u + -2u = -4u
14 + -11u + 2u2 = (4 + -4u + u2)

Solving
14 + -11u + 2u2 = 4 + -4u + u2

Solving for variable 'u'.

Reorder the terms:
14 + -4 + -11u + 4u + 2u2 + -1u2 = 4 + -4u + u2 + -4 + 4u + -1u2

Combine like terms: 14 + -4 = 10
10 + -11u + 4u + 2u2 + -1u2 = 4 + -4u + u2 + -4 + 4u + -1u2

Combine like terms: -11u + 4u = -7u
10 + -7u + 2u2 + -1u2 = 4 + -4u + u2 + -4 + 4u + -1u2

Combine like terms: 2u2 + -1u2 = 1u2
10 + -7u + 1u2 = 4 + -4u + u2 + -4 + 4u + -1u2

Reorder the terms:
10 + -7u + 1u2 = 4 + -4 + -4u + 4u + u2 + -1u2

Combine like terms: 4 + -4 = 0
10 + -7u + 1u2 = 0 + -4u + 4u + u2 + -1u2
10 + -7u + 1u2 = -4u + 4u + u2 + -1u2

Combine like terms: -4u + 4u = 0
10 + -7u + 1u2 = 0 + u2 + -1u2
10 + -7u + 1u2 = u2 + -1u2

Combine like terms: u2 + -1u2 = 0
10 + -7u + 1u2 = 0

Factor a trinomial.
(2 + -1u)(5 + -1u) = 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 + -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
Solution
u = {2, 5}

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