u^2+2u+6u-12=0

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Solution for u^2+2u+6u-12=0 equation:


Simplifying
u2 + 2u + 6u + -12 = 0

Reorder the terms:
-12 + 2u + 6u + u2 = 0

Combine like terms: 2u + 6u = 8u
-12 + 8u + u2 = 0

Solving
-12 + 8u + u2 = 0

Solving for variable 'u'.

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + 8u + 12 + u2 = 0 + 12

Reorder the terms:
-12 + 12 + 8u + u2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 8u + u2 = 0 + 12
8u + u2 = 0 + 12

Combine like terms: 0 + 12 = 12
8u + u2 = 12

The u term is 8u.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8u + 16 + u2 = 12 + 16

Reorder the terms:
16 + 8u + u2 = 12 + 16

Combine like terms: 12 + 16 = 28
16 + 8u + u2 = 28

Factor a perfect square on the left side:
(u + 4)(u + 4) = 28

Calculate the square root of the right side: 5.291502622

Break this problem into two subproblems by setting 
(u + 4) equal to 5.291502622 and -5.291502622.

Subproblem 1

u + 4 = 5.291502622 Simplifying u + 4 = 5.291502622 Reorder the terms: 4 + u = 5.291502622 Solving 4 + u = 5.291502622 Solving for variable 'u'. 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 = 5.291502622 + -4 Combine like terms: 4 + -4 = 0 0 + u = 5.291502622 + -4 u = 5.291502622 + -4 Combine like terms: 5.291502622 + -4 = 1.291502622 u = 1.291502622 Simplifying u = 1.291502622

Subproblem 2

u + 4 = -5.291502622 Simplifying u + 4 = -5.291502622 Reorder the terms: 4 + u = -5.291502622 Solving 4 + u = -5.291502622 Solving for variable 'u'. 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 = -5.291502622 + -4 Combine like terms: 4 + -4 = 0 0 + u = -5.291502622 + -4 u = -5.291502622 + -4 Combine like terms: -5.291502622 + -4 = -9.291502622 u = -9.291502622 Simplifying u = -9.291502622

Solution

The solution to the problem is based on the solutions from the subproblems. u = {1.291502622, -9.291502622}

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