2u^2+13u+15=(u+5)(u+5)

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Solution for 2u^2+13u+15=(u+5)(u+5) equation: 


Simplifying
2u2 + 13u + 15 = (u + 5)(u + 5)

Reorder the terms:
15 + 13u + 2u2 = (u + 5)(u + 5)

Reorder the terms:
15 + 13u + 2u2 = (5 + u)(u + 5)

Reorder the terms:
15 + 13u + 2u2 = (5 + u)(5 + u)

Multiply (5 + u) * (5 + u)
15 + 13u + 2u2 = (5(5 + u) + u(5 + u))
15 + 13u + 2u2 = ((5 * 5 + u * 5) + u(5 + u))
15 + 13u + 2u2 = ((25 + 5u) + u(5 + u))
15 + 13u + 2u2 = (25 + 5u + (5 * u + u * u))
15 + 13u + 2u2 = (25 + 5u + (5u + u2))

Combine like terms: 5u + 5u = 10u
15 + 13u + 2u2 = (25 + 10u + u2)

Solving
15 + 13u + 2u2 = 25 + 10u + u2

Solving for variable 'u'.

Reorder the terms:
15 + -25 + 13u + -10u + 2u2 + -1u2 = 25 + 10u + u2 + -25 + -10u + -1u2

Combine like terms: 15 + -25 = -10
-10 + 13u + -10u + 2u2 + -1u2 = 25 + 10u + u2 + -25 + -10u + -1u2

Combine like terms: 13u + -10u = 3u
-10 + 3u + 2u2 + -1u2 = 25 + 10u + u2 + -25 + -10u + -1u2

Combine like terms: 2u2 + -1u2 = 1u2
-10 + 3u + 1u2 = 25 + 10u + u2 + -25 + -10u + -1u2

Reorder the terms:
-10 + 3u + 1u2 = 25 + -25 + 10u + -10u + u2 + -1u2

Combine like terms: 25 + -25 = 0
-10 + 3u + 1u2 = 0 + 10u + -10u + u2 + -1u2
-10 + 3u + 1u2 = 10u + -10u + u2 + -1u2

Combine like terms: 10u + -10u = 0
-10 + 3u + 1u2 = 0 + u2 + -1u2
-10 + 3u + 1u2 = u2 + -1u2

Combine like terms: u2 + -1u2 = 0
-10 + 3u + 1u2 = 0

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

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