-.2(x+22)(x-15)=0

Solution for -.2(x+22)(x-15)=0 equation:

Simplifying
-0.2(x + 22)(x + -15) = 0

Reorder the terms:
-0.2(22 + x)(x + -15) = 0

Reorder the terms:
-0.2(22 + x)(-15 + x) = 0

Multiply (22 + x) * (-15 + x)
-0.2(22(-15 + x) + x(-15 + x)) = 0
-0.2((-15 * 22 + x * 22) + x(-15 + x)) = 0
-0.2((-330 + 22x) + x(-15 + x)) = 0
-0.2(-330 + 22x + (-15 * x + x * x)) = 0
-0.2(-330 + 22x + (-15x + x2)) = 0

Combine like terms: 22x + -15x = 7x
-0.2(-330 + 7x + x2) = 0
(-330 * -0.2 + 7x * -0.2 + x2 * -0.2) = 0
(66 + -1.4x + -0.2x2) = 0

Solving
66 + -1.4x + -0.2x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.2 the coefficient of the squared term: 

Divide each side by '-0.2'.
-330 + 7x + x2 = 0

Move the constant term to the right:

Add '330' to each side of the equation.
-330 + 7x + 330 + x2 = 0 + 330

Reorder the terms:
-330 + 330 + 7x + x2 = 0 + 330

Combine like terms: -330 + 330 = 0
0 + 7x + x2 = 0 + 330
7x + x2 = 0 + 330

Combine like terms: 0 + 330 = 330
7x + x2 = 330

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 330 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 330 + 12.25

Combine like terms: 330 + 12.25 = 342.25
12.25 + 7x + x2 = 342.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 342.25

Calculate the square root of the right side: 18.5

Break this problem into two subproblems by setting 
(x + 3.5) equal to 18.5 and -18.5.

Subproblem 1
x + 3.5 = 18.5

Simplifying
x + 3.5 = 18.5

Reorder the terms:
3.5 + x = 18.5

Solving
3.5 + x = 18.5

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 18.5 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 18.5 + -3.5
x = 18.5 + -3.5

Combine like terms: 18.5 + -3.5 = 15
x = 15

Simplifying
x = 15

Subproblem 2
x + 3.5 = -18.5

Simplifying
x + 3.5 = -18.5

Reorder the terms:
3.5 + x = -18.5

Solving
3.5 + x = -18.5

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -18.5 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -18.5 + -3.5
x = -18.5 + -3.5

Combine like terms: -18.5 + -3.5 = -22
x = -22

Simplifying
x = -22

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15, -22}