x=0.25*((1.12*(15-1.75*x)-2.5)*(0.85*(15-1.75*x)-2.5))

Solution for x=0.25*((1.12*(15-1.75*x)-2.5)*(0.85*(15-1.75*x)-2.5)) equation:

Simplifying
x = 0.25((1.12(15 + -1.75x) + -2.5)(0.85(15 + -1.75x) + -2.5))
x = 0.25(((15 * 1.12 + -1.75x * 1.12) + -2.5)(0.85(15 + -1.75x) + -2.5))
x = 0.25(((16.8 + -1.96x) + -2.5)(0.85(15 + -1.75x) + -2.5))

Reorder the terms:
x = 0.25((16.8 + -2.5 + -1.96x)(0.85(15 + -1.75x) + -2.5))

Combine like terms: 16.8 + -2.5 = 14.3
x = 0.25((14.3 + -1.96x)(0.85(15 + -1.75x) + -2.5))
x = 0.25((14.3 + -1.96x)((15 * 0.85 + -1.75x * 0.85) + -2.5))
x = 0.25((14.3 + -1.96x)((12.75 + -1.4875x) + -2.5))

Reorder the terms:
x = 0.25((14.3 + -1.96x)(12.75 + -2.5 + -1.4875x))

Combine like terms: 12.75 + -2.5 = 10.25
x = 0.25((14.3 + -1.96x)(10.25 + -1.4875x))

Multiply (14.3 + -1.96x) * (10.25 + -1.4875x)
x = 0.25((14.3(10.25 + -1.4875x) + -1.96x * (10.25 + -1.4875x)))
x = 0.25(((10.25 * 14.3 + -1.4875x * 14.3) + -1.96x * (10.25 + -1.4875x)))
x = 0.25(((146.575 + -21.27125x) + -1.96x * (10.25 + -1.4875x)))
x = 0.25((146.575 + -21.27125x + (10.25 * -1.96x + -1.4875x * -1.96x)))
x = 0.25((146.575 + -21.27125x + (-20.09x + 2.9155x2)))

Combine like terms: -21.27125x + -20.09x = -41.36125x
x = 0.25((146.575 + -41.36125x + 2.9155x2))
x = (146.575 * 0.25 + -41.36125x * 0.25 + 2.9155x2 * 0.25)
x = (36.64375 + -10.3403125x + 0.728875x2)

Solving
x = 36.64375 + -10.3403125x + 0.728875x2

Solving for variable 'x'.

Reorder the terms:
-36.64375 + x + 10.3403125x + -0.728875x2 = 36.64375 + -10.3403125x + 0.728875x2 + -36.64375 + 10.3403125x + -0.728875x2

Combine like terms: x + 10.3403125x = 11.3403125x
-36.64375 + 11.3403125x + -0.728875x2 = 36.64375 + -10.3403125x + 0.728875x2 + -36.64375 + 10.3403125x + -0.728875x2

Reorder the terms:
-36.64375 + 11.3403125x + -0.728875x2 = 36.64375 + -36.64375 + -10.3403125x + 10.3403125x + 0.728875x2 + -0.728875x2

Combine like terms: 36.64375 + -36.64375 = 0.00000
-36.64375 + 11.3403125x + -0.728875x2 = 0.00000 + -10.3403125x + 10.3403125x + 0.728875x2 + -0.728875x2
-36.64375 + 11.3403125x + -0.728875x2 = -10.3403125x + 10.3403125x + 0.728875x2 + -0.728875x2

Combine like terms: -10.3403125x + 10.3403125x = 0.0000000
-36.64375 + 11.3403125x + -0.728875x2 = 0.0000000 + 0.728875x2 + -0.728875x2
-36.64375 + 11.3403125x + -0.728875x2 = 0.728875x2 + -0.728875x2

Combine like terms: 0.728875x2 + -0.728875x2 = 0.000000
-36.64375 + 11.3403125x + -0.728875x2 = 0.000000

Begin completing the square.  Divide all terms by
-0.728875 the coefficient of the squared term: 

Divide each side by '-0.728875'.
50.27439547 + -15.55865203x + x2 = 0

Move the constant term to the right:

Add '-50.27439547' to each side of the equation.
50.27439547 + -15.55865203x + -50.27439547 + x2 = 0 + -50.27439547

Reorder the terms:
50.27439547 + -50.27439547 + -15.55865203x + x2 = 0 + -50.27439547

Combine like terms: 50.27439547 + -50.27439547 = 0.00000000
0.00000000 + -15.55865203x + x2 = 0 + -50.27439547
-15.55865203x + x2 = 0 + -50.27439547

Combine like terms: 0 + -50.27439547 = -50.27439547
-15.55865203x + x2 = -50.27439547

The x term is -15.55865203x.  Take half its coefficient (-7.779326015).
Square it (60.51791325) and add it to both sides.

Add '60.51791325' to each side of the equation.
-15.55865203x + 60.51791325 + x2 = -50.27439547 + 60.51791325

Reorder the terms:
60.51791325 + -15.55865203x + x2 = -50.27439547 + 60.51791325

Combine like terms: -50.27439547 + 60.51791325 = 10.24351778
60.51791325 + -15.55865203x + x2 = 10.24351778

Factor a perfect square on the left side:
(x + -7.779326015)(x + -7.779326015) = 10.24351778

Calculate the square root of the right side: 3.200549606

Break this problem into two subproblems by setting 
(x + -7.779326015) equal to 3.200549606 and -3.200549606.

Subproblem 1
x + -7.779326015 = 3.200549606

Simplifying
x + -7.779326015 = 3.200549606

Reorder the terms:
-7.779326015 + x = 3.200549606

Solving
-7.779326015 + x = 3.200549606

Solving for variable 'x'.

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

Add '7.779326015' to each side of the equation.
-7.779326015 + 7.779326015 + x = 3.200549606 + 7.779326015

Combine like terms: -7.779326015 + 7.779326015 = 0.000000000
0.000000000 + x = 3.200549606 + 7.779326015
x = 3.200549606 + 7.779326015

Combine like terms: 3.200549606 + 7.779326015 = 10.979875621
x = 10.979875621

Simplifying
x = 10.979875621

Subproblem 2
x + -7.779326015 = -3.200549606

Simplifying
x + -7.779326015 = -3.200549606

Reorder the terms:
-7.779326015 + x = -3.200549606

Solving
-7.779326015 + x = -3.200549606

Solving for variable 'x'.

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

Add '7.779326015' to each side of the equation.
-7.779326015 + 7.779326015 + x = -3.200549606 + 7.779326015

Combine like terms: -7.779326015 + 7.779326015 = 0.000000000
0.000000000 + x = -3.200549606 + 7.779326015
x = -3.200549606 + 7.779326015

Combine like terms: -3.200549606 + 7.779326015 = 4.578776409
x = 4.578776409

Simplifying
x = 4.578776409

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.979875621, 4.578776409}