2u^2-16u+31=(u-6)(u-6)

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Solution for 2u^2-16u+31=(u-6)(u-6) equation: 


Simplifying
2u2 + -16u + 31 = (u + -6)(u + -6)

Reorder the terms:
31 + -16u + 2u2 = (u + -6)(u + -6)

Reorder the terms:
31 + -16u + 2u2 = (-6 + u)(u + -6)

Reorder the terms:
31 + -16u + 2u2 = (-6 + u)(-6 + u)

Multiply (-6 + u) * (-6 + u)
31 + -16u + 2u2 = (-6(-6 + u) + u(-6 + u))
31 + -16u + 2u2 = ((-6 * -6 + u * -6) + u(-6 + u))
31 + -16u + 2u2 = ((36 + -6u) + u(-6 + u))
31 + -16u + 2u2 = (36 + -6u + (-6 * u + u * u))
31 + -16u + 2u2 = (36 + -6u + (-6u + u2))

Combine like terms: -6u + -6u = -12u
31 + -16u + 2u2 = (36 + -12u + u2)

Solving
31 + -16u + 2u2 = 36 + -12u + u2

Solving for variable 'u'.

Reorder the terms:
31 + -36 + -16u + 12u + 2u2 + -1u2 = 36 + -12u + u2 + -36 + 12u + -1u2

Combine like terms: 31 + -36 = -5
-5 + -16u + 12u + 2u2 + -1u2 = 36 + -12u + u2 + -36 + 12u + -1u2

Combine like terms: -16u + 12u = -4u
-5 + -4u + 2u2 + -1u2 = 36 + -12u + u2 + -36 + 12u + -1u2

Combine like terms: 2u2 + -1u2 = 1u2
-5 + -4u + 1u2 = 36 + -12u + u2 + -36 + 12u + -1u2

Reorder the terms:
-5 + -4u + 1u2 = 36 + -36 + -12u + 12u + u2 + -1u2

Combine like terms: 36 + -36 = 0
-5 + -4u + 1u2 = 0 + -12u + 12u + u2 + -1u2
-5 + -4u + 1u2 = -12u + 12u + u2 + -1u2

Combine like terms: -12u + 12u = 0
-5 + -4u + 1u2 = 0 + u2 + -1u2
-5 + -4u + 1u2 = u2 + -1u2

Combine like terms: u2 + -1u2 = 0
-5 + -4u + 1u2 = 0

Factor a trinomial.
(-1 + -1u)(5 + -1u) = 0


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

Simplifying
-1 + -1u = 0

Solving
-1 + -1u = 0

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

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

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

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

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

Simplifying
u = -1

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 = {-1, 5}

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