6u(2-u)=-7

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Solution for 6u(2-u)=-7 equation:


Simplifying
6u(2 + -1u) = -7
(2 * 6u + -1u * 6u) = -7
(12u + -6u2) = -7

Solving
12u + -6u2 = -7

Solving for variable 'u'.

Reorder the terms:
7 + 12u + -6u2 = -7 + 7

Combine like terms: -7 + 7 = 0
7 + 12u + -6u2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
-1.166666667 + -2u + u2 = 0

Move the constant term to the right:

Add '1.166666667' to each side of the equation.
-1.166666667 + -2u + 1.166666667 + u2 = 0 + 1.166666667

Reorder the terms:
-1.166666667 + 1.166666667 + -2u + u2 = 0 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + -2u + u2 = 0 + 1.166666667
-2u + u2 = 0 + 1.166666667

Combine like terms: 0 + 1.166666667 = 1.166666667
-2u + u2 = 1.166666667

The u term is -2u.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2u + 1 + u2 = 1.166666667 + 1

Reorder the terms:
1 + -2u + u2 = 1.166666667 + 1

Combine like terms: 1.166666667 + 1 = 2.166666667
1 + -2u + u2 = 2.166666667

Factor a perfect square on the left side:
(u + -1)(u + -1) = 2.166666667

Calculate the square root of the right side: 1.471960145

Break this problem into two subproblems by setting 
(u + -1) equal to 1.471960145 and -1.471960145.

Subproblem 1

u + -1 = 1.471960145 Simplifying u + -1 = 1.471960145 Reorder the terms: -1 + u = 1.471960145 Solving -1 + u = 1.471960145 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + u = 1.471960145 + 1 Combine like terms: -1 + 1 = 0 0 + u = 1.471960145 + 1 u = 1.471960145 + 1 Combine like terms: 1.471960145 + 1 = 2.471960145 u = 2.471960145 Simplifying u = 2.471960145

Subproblem 2

u + -1 = -1.471960145 Simplifying u + -1 = -1.471960145 Reorder the terms: -1 + u = -1.471960145 Solving -1 + u = -1.471960145 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + u = -1.471960145 + 1 Combine like terms: -1 + 1 = 0 0 + u = -1.471960145 + 1 u = -1.471960145 + 1 Combine like terms: -1.471960145 + 1 = -0.471960145 u = -0.471960145 Simplifying u = -0.471960145

Solution

The solution to the problem is based on the solutions from the subproblems. u = {2.471960145, -0.471960145}

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