.2(x-7)(x-9)=0

Solution for .2(x-7)(x-9)=0 equation:

Simplifying
0.2(x + -7)(x + -9) = 0

Reorder the terms:
0.2(-7 + x)(x + -9) = 0

Reorder the terms:
0.2(-7 + x)(-9 + x) = 0

Multiply (-7 + x) * (-9 + x)
0.2(-7(-9 + x) + x(-9 + x)) = 0
0.2((-9 * -7 + x * -7) + x(-9 + x)) = 0
0.2((63 + -7x) + x(-9 + x)) = 0
0.2(63 + -7x + (-9 * x + x * x)) = 0
0.2(63 + -7x + (-9x + x2)) = 0

Combine like terms: -7x + -9x = -16x
0.2(63 + -16x + x2) = 0
(63 * 0.2 + -16x * 0.2 + x2 * 0.2) = 0
(12.6 + -3.2x + 0.2x2) = 0

Solving
12.6 + -3.2x + 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'.
63 + -16x + x2 = 0

Move the constant term to the right:

Add '-63' to each side of the equation.
63 + -16x + -63 + x2 = 0 + -63

Reorder the terms:
63 + -63 + -16x + x2 = 0 + -63

Combine like terms: 63 + -63 = 0
0 + -16x + x2 = 0 + -63
-16x + x2 = 0 + -63

Combine like terms: 0 + -63 = -63
-16x + x2 = -63

The x term is -16x.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16x + 64 + x2 = -63 + 64

Reorder the terms:
64 + -16x + x2 = -63 + 64

Combine like terms: -63 + 64 = 1
64 + -16x + x2 = 1

Factor a perfect square on the left side:
(x + -8)(x + -8) = 1

Calculate the square root of the right side: 1

Break this problem into two subproblems by setting 
(x + -8) equal to 1 and -1.

Subproblem 1
x + -8 = 1

Simplifying
x + -8 = 1

Reorder the terms:
-8 + x = 1

Solving
-8 + x = 1

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x = 1 + 8

Combine like terms: -8 + 8 = 0
0 + x = 1 + 8
x = 1 + 8

Combine like terms: 1 + 8 = 9
x = 9

Simplifying
x = 9

Subproblem 2
x + -8 = -1

Simplifying
x + -8 = -1

Reorder the terms:
-8 + x = -1

Solving
-8 + x = -1

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x = -1 + 8

Combine like terms: -8 + 8 = 0
0 + x = -1 + 8
x = -1 + 8

Combine like terms: -1 + 8 = 7
x = 7

Simplifying
x = 7

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9, 7}