2u^2+u+53=(u-5)(u-5)

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Solution for 2u^2+u+53=(u-5)(u-5) equation: 


Simplifying
2u2 + u + 53 = (u + -5)(u + -5)

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

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

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

Multiply (-5 + u) * (-5 + u)
53 + u + 2u2 = (-5(-5 + u) + u(-5 + u))
53 + u + 2u2 = ((-5 * -5 + u * -5) + u(-5 + u))
53 + u + 2u2 = ((25 + -5u) + u(-5 + u))
53 + u + 2u2 = (25 + -5u + (-5 * u + u * u))
53 + u + 2u2 = (25 + -5u + (-5u + u2))

Combine like terms: -5u + -5u = -10u
53 + u + 2u2 = (25 + -10u + u2)

Solving
53 + u + 2u2 = 25 + -10u + u2

Solving for variable 'u'.

Reorder the terms:
53 + -25 + u + 10u + 2u2 + -1u2 = 25 + -10u + u2 + -25 + 10u + -1u2

Combine like terms: 53 + -25 = 28
28 + u + 10u + 2u2 + -1u2 = 25 + -10u + u2 + -25 + 10u + -1u2

Combine like terms: u + 10u = 11u
28 + 11u + 2u2 + -1u2 = 25 + -10u + u2 + -25 + 10u + -1u2

Combine like terms: 2u2 + -1u2 = 1u2
28 + 11u + 1u2 = 25 + -10u + u2 + -25 + 10u + -1u2

Reorder the terms:
28 + 11u + 1u2 = 25 + -25 + -10u + 10u + u2 + -1u2

Combine like terms: 25 + -25 = 0
28 + 11u + 1u2 = 0 + -10u + 10u + u2 + -1u2
28 + 11u + 1u2 = -10u + 10u + u2 + -1u2

Combine like terms: -10u + 10u = 0
28 + 11u + 1u2 = 0 + u2 + -1u2
28 + 11u + 1u2 = u2 + -1u2

Combine like terms: u2 + -1u2 = 0
28 + 11u + 1u2 = 0

Factor a trinomial.
(7 + u)(4 + u) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(4 + u)' equal to zero and attempt to solve:

Simplifying
4 + u = 0

Solving
4 + u = 0

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

Add '-4' to each side of the equation.
4 + -4 + u = 0 + -4

Combine like terms: 4 + -4 = 0
0 + u = 0 + -4
u = 0 + -4

Combine like terms: 0 + -4 = -4
u = -4

Simplifying
u = -4
Solution
u = {-7, -4}

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