0.92x+0.98x(12-x)=0.96(12)

Solution for 0.92x+0.98x(12-x)=0.96(12) equation:

Simplifying
0.92x + 0.98x(12 + -1x) = 0.96(12)
0.92x + (12 * 0.98x + -1x * 0.98x) = 0.96(12)
0.92x + (11.76x + -0.98x2) = 0.96(12)

Combine like terms: 0.92x + 11.76x = 12.68x
12.68x + -0.98x2 = 0.96(12)

Multiply 0.96 * 12
12.68x + -0.98x2 = 11.52

Solving
12.68x + -0.98x2 = 11.52

Solving for variable 'x'.

Reorder the terms:
-11.52 + 12.68x + -0.98x2 = 11.52 + -11.52

Combine like terms: 11.52 + -11.52 = 0.00
-11.52 + 12.68x + -0.98x2 = 0.00

Begin completing the square.  Divide all terms by
-0.98 the coefficient of the squared term: 

Divide each side by '-0.98'.
11.75510204 + -12.93877551x + x2 = 0

Move the constant term to the right:

Add '-11.75510204' to each side of the equation.
11.75510204 + -12.93877551x + -11.75510204 + x2 = 0 + -11.75510204

Reorder the terms:
11.75510204 + -11.75510204 + -12.93877551x + x2 = 0 + -11.75510204

Combine like terms: 11.75510204 + -11.75510204 = 0.00000000
0.00000000 + -12.93877551x + x2 = 0 + -11.75510204
-12.93877551x + x2 = 0 + -11.75510204

Combine like terms: 0 + -11.75510204 = -11.75510204
-12.93877551x + x2 = -11.75510204

The x term is -12.93877551x.  Take half its coefficient (-6.469387755).
Square it (41.85297792) and add it to both sides.

Add '41.85297792' to each side of the equation.
-12.93877551x + 41.85297792 + x2 = -11.75510204 + 41.85297792

Reorder the terms:
41.85297792 + -12.93877551x + x2 = -11.75510204 + 41.85297792

Combine like terms: -11.75510204 + 41.85297792 = 30.09787588
41.85297792 + -12.93877551x + x2 = 30.09787588

Factor a perfect square on the left side:
(x + -6.469387755)(x + -6.469387755) = 30.09787588

Calculate the square root of the right side: 5.486153104

Break this problem into two subproblems by setting 
(x + -6.469387755) equal to 5.486153104 and -5.486153104.

Subproblem 1
x + -6.469387755 = 5.486153104

Simplifying
x + -6.469387755 = 5.486153104

Reorder the terms:
-6.469387755 + x = 5.486153104

Solving
-6.469387755 + x = 5.486153104

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '6.469387755' to each side of the equation.
-6.469387755 + 6.469387755 + x = 5.486153104 + 6.469387755

Combine like terms: -6.469387755 + 6.469387755 = 0.000000000
0.000000000 + x = 5.486153104 + 6.469387755
x = 5.486153104 + 6.469387755

Combine like terms: 5.486153104 + 6.469387755 = 11.955540859
x = 11.955540859

Simplifying
x = 11.955540859

Subproblem 2
x + -6.469387755 = -5.486153104

Simplifying
x + -6.469387755 = -5.486153104

Reorder the terms:
-6.469387755 + x = -5.486153104

Solving
-6.469387755 + x = -5.486153104

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '6.469387755' to each side of the equation.
-6.469387755 + 6.469387755 + x = -5.486153104 + 6.469387755

Combine like terms: -6.469387755 + 6.469387755 = 0.000000000
0.000000000 + x = -5.486153104 + 6.469387755
x = -5.486153104 + 6.469387755

Combine like terms: -5.486153104 + 6.469387755 = 0.983234651
x = 0.983234651

Simplifying
x = 0.983234651

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.955540859, 0.983234651}