2u^2+10u+1=(u+4)(u+4)

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Solution for 2u^2+10u+1=(u+4)(u+4) equation: 


Simplifying
2u2 + 10u + 1 = (u + 4)(u + 4)

Reorder the terms:
1 + 10u + 2u2 = (u + 4)(u + 4)

Reorder the terms:
1 + 10u + 2u2 = (4 + u)(u + 4)

Reorder the terms:
1 + 10u + 2u2 = (4 + u)(4 + u)

Multiply (4 + u) * (4 + u)
1 + 10u + 2u2 = (4(4 + u) + u(4 + u))
1 + 10u + 2u2 = ((4 * 4 + u * 4) + u(4 + u))
1 + 10u + 2u2 = ((16 + 4u) + u(4 + u))
1 + 10u + 2u2 = (16 + 4u + (4 * u + u * u))
1 + 10u + 2u2 = (16 + 4u + (4u + u2))

Combine like terms: 4u + 4u = 8u
1 + 10u + 2u2 = (16 + 8u + u2)

Solving
1 + 10u + 2u2 = 16 + 8u + u2

Solving for variable 'u'.

Reorder the terms:
1 + -16 + 10u + -8u + 2u2 + -1u2 = 16 + 8u + u2 + -16 + -8u + -1u2

Combine like terms: 1 + -16 = -15
-15 + 10u + -8u + 2u2 + -1u2 = 16 + 8u + u2 + -16 + -8u + -1u2

Combine like terms: 10u + -8u = 2u
-15 + 2u + 2u2 + -1u2 = 16 + 8u + u2 + -16 + -8u + -1u2

Combine like terms: 2u2 + -1u2 = 1u2
-15 + 2u + 1u2 = 16 + 8u + u2 + -16 + -8u + -1u2

Reorder the terms:
-15 + 2u + 1u2 = 16 + -16 + 8u + -8u + u2 + -1u2

Combine like terms: 16 + -16 = 0
-15 + 2u + 1u2 = 0 + 8u + -8u + u2 + -1u2
-15 + 2u + 1u2 = 8u + -8u + u2 + -1u2

Combine like terms: 8u + -8u = 0
-15 + 2u + 1u2 = 0 + u2 + -1u2
-15 + 2u + 1u2 = u2 + -1u2

Combine like terms: u2 + -1u2 = 0
-15 + 2u + 1u2 = 0

Factor a trinomial.
(-5 + -1u)(3 + -1u) = 0


Subproblem 1
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

Subproblem 2
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
Solution
u = {-5, 3}

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