(3.2)(-x)=9.5(1.0+x)(1.2+x)

Solution for (3.2)(-x)=9.5(1.0+x)(1.2+x) equation:

Simplifying
(3.2)(-1x) = 9.5(1.0 + x)(1.2 + x)

Remove parenthesis around (-1x)
3.2 * -1x = 9.5(1.0 + x)(1.2 + x)

Multiply 3.2 * -1
-3.2x = 9.5(1.0 + x)(1.2 + x)

Multiply (1.0 + x) * (1.2 + x)
-3.2x = 9.5(1.0(1.2 + x) + x(1.2 + x))
-3.2x = 9.5((1.2 * 1.0 + x * 1.0) + x(1.2 + x))
-3.2x = 9.5((1.2 + 1.0x) + x(1.2 + x))
-3.2x = 9.5(1.2 + 1.0x + (1.2 * x + x * x))
-3.2x = 9.5(1.2 + 1.0x + (1.2x + x2))

Combine like terms: 1.0x + 1.2x = 2.2x
-3.2x = 9.5(1.2 + 2.2x + x2)
-3.2x = (1.2 * 9.5 + 2.2x * 9.5 + x2 * 9.5)
-3.2x = (11.4 + 20.9x + 9.5x2)

Solving
-3.2x = 11.4 + 20.9x + 9.5x2

Solving for variable 'x'.

Reorder the terms:
-11.4 + -3.2x + -20.9x + -9.5x2 = 11.4 + 20.9x + 9.5x2 + -11.4 + -20.9x + -9.5x2

Combine like terms: -3.2x + -20.9x = -24.1x
-11.4 + -24.1x + -9.5x2 = 11.4 + 20.9x + 9.5x2 + -11.4 + -20.9x + -9.5x2

Reorder the terms:
-11.4 + -24.1x + -9.5x2 = 11.4 + -11.4 + 20.9x + -20.9x + 9.5x2 + -9.5x2

Combine like terms: 11.4 + -11.4 = 0.0
-11.4 + -24.1x + -9.5x2 = 0.0 + 20.9x + -20.9x + 9.5x2 + -9.5x2
-11.4 + -24.1x + -9.5x2 = 20.9x + -20.9x + 9.5x2 + -9.5x2

Combine like terms: 20.9x + -20.9x = 0.0
-11.4 + -24.1x + -9.5x2 = 0.0 + 9.5x2 + -9.5x2
-11.4 + -24.1x + -9.5x2 = 9.5x2 + -9.5x2

Combine like terms: 9.5x2 + -9.5x2 = 0.0
-11.4 + -24.1x + -9.5x2 = 0.0

Begin completing the square.  Divide all terms by
-9.5 the coefficient of the squared term: 

Divide each side by '-9.5'.
1.2 + 2.536842105x + x2 = 0

Move the constant term to the right:

Add '-1.2' to each side of the equation.
1.2 + 2.536842105x + -1.2 + x2 = 0 + -1.2

Reorder the terms:
1.2 + -1.2 + 2.536842105x + x2 = 0 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + 2.536842105x + x2 = 0 + -1.2
2.536842105x + x2 = 0 + -1.2

Combine like terms: 0 + -1.2 = -1.2
2.536842105x + x2 = -1.2

The x term is 2.536842105x.  Take half its coefficient (1.268421053).
Square it (1.608891968) and add it to both sides.

Add '1.608891968' to each side of the equation.
2.536842105x + 1.608891968 + x2 = -1.2 + 1.608891968

Reorder the terms:
1.608891968 + 2.536842105x + x2 = -1.2 + 1.608891968

Combine like terms: -1.2 + 1.608891968 = 0.408891968
1.608891968 + 2.536842105x + x2 = 0.408891968

Factor a perfect square on the left side:
(x + 1.268421053)(x + 1.268421053) = 0.408891968

Calculate the square root of the right side: 0.639446611

Break this problem into two subproblems by setting 
(x + 1.268421053) equal to 0.639446611 and -0.639446611.

Subproblem 1
x + 1.268421053 = 0.639446611

Simplifying
x + 1.268421053 = 0.639446611

Reorder the terms:
1.268421053 + x = 0.639446611

Solving
1.268421053 + x = 0.639446611

Solving for variable 'x'.

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

Add '-1.268421053' to each side of the equation.
1.268421053 + -1.268421053 + x = 0.639446611 + -1.268421053

Combine like terms: 1.268421053 + -1.268421053 = 0.000000000
0.000000000 + x = 0.639446611 + -1.268421053
x = 0.639446611 + -1.268421053

Combine like terms: 0.639446611 + -1.268421053 = -0.628974442
x = -0.628974442

Simplifying
x = -0.628974442

Subproblem 2
x + 1.268421053 = -0.639446611

Simplifying
x + 1.268421053 = -0.639446611

Reorder the terms:
1.268421053 + x = -0.639446611

Solving
1.268421053 + x = -0.639446611

Solving for variable 'x'.

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

Add '-1.268421053' to each side of the equation.
1.268421053 + -1.268421053 + x = -0.639446611 + -1.268421053

Combine like terms: 1.268421053 + -1.268421053 = 0.000000000
0.000000000 + x = -0.639446611 + -1.268421053
x = -0.639446611 + -1.268421053

Combine like terms: -0.639446611 + -1.268421053 = -1.907867664
x = -1.907867664

Simplifying
x = -1.907867664

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.628974442, -1.907867664}