(5x-10)(2x-14)=18

Solution for (5x-10)(2x-14)=18 equation:

Simplifying
(5x + -10)(2x + -14) = 18

Reorder the terms:
(-10 + 5x)(2x + -14) = 18

Reorder the terms:
(-10 + 5x)(-14 + 2x) = 18

Multiply (-10 + 5x) * (-14 + 2x)
(-10(-14 + 2x) + 5x * (-14 + 2x)) = 18
((-14 * -10 + 2x * -10) + 5x * (-14 + 2x)) = 18
((140 + -20x) + 5x * (-14 + 2x)) = 18
(140 + -20x + (-14 * 5x + 2x * 5x)) = 18
(140 + -20x + (-70x + 10x2)) = 18

Combine like terms: -20x + -70x = -90x
(140 + -90x + 10x2) = 18

Solving
140 + -90x + 10x2 = 18

Solving for variable 'x'.

Reorder the terms:
140 + -18 + -90x + 10x2 = 18 + -18

Combine like terms: 140 + -18 = 122
122 + -90x + 10x2 = 18 + -18

Combine like terms: 18 + -18 = 0
122 + -90x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(61 + -45x + 5x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(61 + -45x + 5x2)' equal to zero and attempt to solve:

Simplifying
61 + -45x + 5x2 = 0

Solving
61 + -45x + 5x2 = 0

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

Divide each side by '5'.
12.2 + -9x + x2 = 0

Move the constant term to the right:

Add '-12.2' to each side of the equation.
12.2 + -9x + -12.2 + x2 = 0 + -12.2

Reorder the terms:
12.2 + -12.2 + -9x + x2 = 0 + -12.2

Combine like terms: 12.2 + -12.2 = 0.0
0.0 + -9x + x2 = 0 + -12.2
-9x + x2 = 0 + -12.2

Combine like terms: 0 + -12.2 = -12.2
-9x + x2 = -12.2

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = -12.2 + 20.25

Reorder the terms:
20.25 + -9x + x2 = -12.2 + 20.25

Combine like terms: -12.2 + 20.25 = 8.05
20.25 + -9x + x2 = 8.05

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 8.05

Calculate the square root of the right side: 2.837252192

Break this problem into two subproblems by setting 
(x + -4.5) equal to 2.837252192 and -2.837252192.

Subproblem 1
x + -4.5 = 2.837252192

Simplifying
x + -4.5 = 2.837252192

Reorder the terms:
-4.5 + x = 2.837252192

Solving
-4.5 + x = 2.837252192

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = 2.837252192 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = 2.837252192 + 4.5
x = 2.837252192 + 4.5

Combine like terms: 2.837252192 + 4.5 = 7.337252192
x = 7.337252192

Simplifying
x = 7.337252192

Subproblem 2
x + -4.5 = -2.837252192

Simplifying
x + -4.5 = -2.837252192

Reorder the terms:
-4.5 + x = -2.837252192

Solving
-4.5 + x = -2.837252192

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = -2.837252192 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = -2.837252192 + 4.5
x = -2.837252192 + 4.5

Combine like terms: -2.837252192 + 4.5 = 1.662747808
x = 1.662747808

Simplifying
x = 1.662747808

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.337252192, 1.662747808}
Solution
x = {7.337252192, 1.662747808}