(5x-9)(6x-15)=90

Solution for (5x-9)(6x-15)=90 equation:

Simplifying
(5x + -9)(6x + -15) = 90

Reorder the terms:
(-9 + 5x)(6x + -15) = 90

Reorder the terms:
(-9 + 5x)(-15 + 6x) = 90

Multiply (-9 + 5x) * (-15 + 6x)
(-9(-15 + 6x) + 5x * (-15 + 6x)) = 90
((-15 * -9 + 6x * -9) + 5x * (-15 + 6x)) = 90
((135 + -54x) + 5x * (-15 + 6x)) = 90
(135 + -54x + (-15 * 5x + 6x * 5x)) = 90
(135 + -54x + (-75x + 30x2)) = 90

Combine like terms: -54x + -75x = -129x
(135 + -129x + 30x2) = 90

Solving
135 + -129x + 30x2 = 90

Solving for variable 'x'.

Reorder the terms:
135 + -90 + -129x + 30x2 = 90 + -90

Combine like terms: 135 + -90 = 45
45 + -129x + 30x2 = 90 + -90

Combine like terms: 90 + -90 = 0
45 + -129x + 30x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(15 + -43x + 10x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(15 + -43x + 10x2)' equal to zero and attempt to solve:

Simplifying
15 + -43x + 10x2 = 0

Solving
15 + -43x + 10x2 = 0

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

Divide each side by '10'.
1.5 + -4.3x + x2 = 0.0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -4.3x + -1.5 + x2 = 0.0 + -1.5

Reorder the terms:
1.5 + -1.5 + -4.3x + x2 = 0.0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -4.3x + x2 = 0.0 + -1.5
-4.3x + x2 = 0.0 + -1.5

Combine like terms: 0.0 + -1.5 = -1.5
-4.3x + x2 = -1.5

The x term is -4.3x.  Take half its coefficient (-2.15).
Square it (4.6225) and add it to both sides.

Add '4.6225' to each side of the equation.
-4.3x + 4.6225 + x2 = -1.5 + 4.6225

Reorder the terms:
4.6225 + -4.3x + x2 = -1.5 + 4.6225

Combine like terms: -1.5 + 4.6225 = 3.1225
4.6225 + -4.3x + x2 = 3.1225

Factor a perfect square on the left side:
(x + -2.15)(x + -2.15) = 3.1225

Calculate the square root of the right side: 1.767059705

Break this problem into two subproblems by setting 
(x + -2.15) equal to 1.767059705 and -1.767059705.

Subproblem 1
x + -2.15 = 1.767059705

Simplifying
x + -2.15 = 1.767059705

Reorder the terms:
-2.15 + x = 1.767059705

Solving
-2.15 + x = 1.767059705

Solving for variable 'x'.

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

Add '2.15' to each side of the equation.
-2.15 + 2.15 + x = 1.767059705 + 2.15

Combine like terms: -2.15 + 2.15 = 0.00
0.00 + x = 1.767059705 + 2.15
x = 1.767059705 + 2.15

Combine like terms: 1.767059705 + 2.15 = 3.917059705
x = 3.917059705

Simplifying
x = 3.917059705

Subproblem 2
x + -2.15 = -1.767059705

Simplifying
x + -2.15 = -1.767059705

Reorder the terms:
-2.15 + x = -1.767059705

Solving
-2.15 + x = -1.767059705

Solving for variable 'x'.

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

Add '2.15' to each side of the equation.
-2.15 + 2.15 + x = -1.767059705 + 2.15

Combine like terms: -2.15 + 2.15 = 0.00
0.00 + x = -1.767059705 + 2.15
x = -1.767059705 + 2.15

Combine like terms: -1.767059705 + 2.15 = 0.382940295
x = 0.382940295

Simplifying
x = 0.382940295

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.917059705, 0.382940295}
Solution
x = {3.917059705, 0.382940295}