32.87(.08-x)=1.50+1.50x(.08-x)

Solution for 32.87(.08-x)=1.50+1.50x(.08-x) equation:

Simplifying
32.87(0.08 + -1x) = 1.50 + 1.50x(0.08 + -1x)
(0.08 * 32.87 + -1x * 32.87) = 1.50 + 1.50x(0.08 + -1x)
(2.6296 + -32.87x) = 1.50 + 1.50x(0.08 + -1x)
2.6296 + -32.87x = 1.50 + (0.08 * 1.50x + -1x * 1.50x)
2.6296 + -32.87x = 1.50 + (0.12x + -1.5x2)

Solving
2.6296 + -32.87x = 1.50 + 0.12x + -1.5x2

Solving for variable 'x'.

Reorder the terms:
2.6296 + -1.50 + -32.87x + -0.12x + 1.5x2 = 1.50 + 0.12x + -1.5x2 + -1.50 + -0.12x + 1.5x2

Combine like terms: 2.6296 + -1.50 = 1.1296
1.1296 + -32.87x + -0.12x + 1.5x2 = 1.50 + 0.12x + -1.5x2 + -1.50 + -0.12x + 1.5x2

Combine like terms: -32.87x + -0.12x = -32.99x
1.1296 + -32.99x + 1.5x2 = 1.50 + 0.12x + -1.5x2 + -1.50 + -0.12x + 1.5x2

Reorder the terms:
1.1296 + -32.99x + 1.5x2 = 1.50 + -1.50 + 0.12x + -0.12x + -1.5x2 + 1.5x2

Combine like terms: 1.50 + -1.50 = 0.00
1.1296 + -32.99x + 1.5x2 = 0.00 + 0.12x + -0.12x + -1.5x2 + 1.5x2
1.1296 + -32.99x + 1.5x2 = 0.12x + -0.12x + -1.5x2 + 1.5x2

Combine like terms: 0.12x + -0.12x = 0.00
1.1296 + -32.99x + 1.5x2 = 0.00 + -1.5x2 + 1.5x2
1.1296 + -32.99x + 1.5x2 = -1.5x2 + 1.5x2

Combine like terms: -1.5x2 + 1.5x2 = 0.0
1.1296 + -32.99x + 1.5x2 = 0.0

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

Divide each side by '1.5'.
0.7530666667 + -21.99333333x + x2 = 0

Move the constant term to the right:

Add '-0.7530666667' to each side of the equation.
0.7530666667 + -21.99333333x + -0.7530666667 + x2 = 0 + -0.7530666667

Reorder the terms:
0.7530666667 + -0.7530666667 + -21.99333333x + x2 = 0 + -0.7530666667

Combine like terms: 0.7530666667 + -0.7530666667 = 0.0000000000
0.0000000000 + -21.99333333x + x2 = 0 + -0.7530666667
-21.99333333x + x2 = 0 + -0.7530666667

Combine like terms: 0 + -0.7530666667 = -0.7530666667
-21.99333333x + x2 = -0.7530666667

The x term is -21.99333333x.  Take half its coefficient (-10.99666667).
Square it (120.9266779) and add it to both sides.

Add '120.9266779' to each side of the equation.
-21.99333333x + 120.9266779 + x2 = -0.7530666667 + 120.9266779

Reorder the terms:
120.9266779 + -21.99333333x + x2 = -0.7530666667 + 120.9266779

Combine like terms: -0.7530666667 + 120.9266779 = 120.1736112333
120.9266779 + -21.99333333x + x2 = 120.1736112333

Factor a perfect square on the left side:
(x + -10.99666667)(x + -10.99666667) = 120.1736112333

Calculate the square root of the right side: 10.962372518

Break this problem into two subproblems by setting 
(x + -10.99666667) equal to 10.962372518 and -10.962372518.

Subproblem 1
x + -10.99666667 = 10.962372518

Simplifying
x + -10.99666667 = 10.962372518

Reorder the terms:
-10.99666667 + x = 10.962372518

Solving
-10.99666667 + x = 10.962372518

Solving for variable 'x'.

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

Add '10.99666667' to each side of the equation.
-10.99666667 + 10.99666667 + x = 10.962372518 + 10.99666667

Combine like terms: -10.99666667 + 10.99666667 = 0.00000000
0.00000000 + x = 10.962372518 + 10.99666667
x = 10.962372518 + 10.99666667

Combine like terms: 10.962372518 + 10.99666667 = 21.959039188
x = 21.959039188

Simplifying
x = 21.959039188

Subproblem 2
x + -10.99666667 = -10.962372518

Simplifying
x + -10.99666667 = -10.962372518

Reorder the terms:
-10.99666667 + x = -10.962372518

Solving
-10.99666667 + x = -10.962372518

Solving for variable 'x'.

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

Add '10.99666667' to each side of the equation.
-10.99666667 + 10.99666667 + x = -10.962372518 + 10.99666667

Combine like terms: -10.99666667 + 10.99666667 = 0.00000000
0.00000000 + x = -10.962372518 + 10.99666667
x = -10.962372518 + 10.99666667

Combine like terms: -10.962372518 + 10.99666667 = 0.034294152
x = 0.034294152

Simplifying
x = 0.034294152

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {21.959039188, 0.034294152}