2u^2-7u+15=(u+1)(u+1)

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Solution for 2u^2-7u+15=(u+1)(u+1) equation: 


Simplifying
2u2 + -7u + 15 = (u + 1)(u + 1)

Reorder the terms:
15 + -7u + 2u2 = (u + 1)(u + 1)

Reorder the terms:
15 + -7u + 2u2 = (1 + u)(u + 1)

Reorder the terms:
15 + -7u + 2u2 = (1 + u)(1 + u)

Multiply (1 + u) * (1 + u)
15 + -7u + 2u2 = (1(1 + u) + u(1 + u))
15 + -7u + 2u2 = ((1 * 1 + u * 1) + u(1 + u))
15 + -7u + 2u2 = ((1 + 1u) + u(1 + u))
15 + -7u + 2u2 = (1 + 1u + (1 * u + u * u))
15 + -7u + 2u2 = (1 + 1u + (1u + u2))

Combine like terms: 1u + 1u = 2u
15 + -7u + 2u2 = (1 + 2u + u2)

Solving
15 + -7u + 2u2 = 1 + 2u + u2

Solving for variable 'u'.

Reorder the terms:
15 + -1 + -7u + -2u + 2u2 + -1u2 = 1 + 2u + u2 + -1 + -2u + -1u2

Combine like terms: 15 + -1 = 14
14 + -7u + -2u + 2u2 + -1u2 = 1 + 2u + u2 + -1 + -2u + -1u2

Combine like terms: -7u + -2u = -9u
14 + -9u + 2u2 + -1u2 = 1 + 2u + u2 + -1 + -2u + -1u2

Combine like terms: 2u2 + -1u2 = 1u2
14 + -9u + 1u2 = 1 + 2u + u2 + -1 + -2u + -1u2

Reorder the terms:
14 + -9u + 1u2 = 1 + -1 + 2u + -2u + u2 + -1u2

Combine like terms: 1 + -1 = 0
14 + -9u + 1u2 = 0 + 2u + -2u + u2 + -1u2
14 + -9u + 1u2 = 2u + -2u + u2 + -1u2

Combine like terms: 2u + -2u = 0
14 + -9u + 1u2 = 0 + u2 + -1u2
14 + -9u + 1u2 = u2 + -1u2

Combine like terms: u2 + -1u2 = 0
14 + -9u + 1u2 = 0

Factor a trinomial.
(2 + -1u)(7 + -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 '(7 + -1u)' equal to zero and attempt to solve:

Simplifying
7 + -1u = 0

Solving
7 + -1u = 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 + -1u = 0 + -7

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

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

Divide each side by '-1'.
u = 7

Simplifying
u = 7
Solution
u = {2, 7}

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