(x-10)(4x-10)=90

Solution for (x-10)(4x-10)=90 equation:

Simplifying
(x + -10)(4x + -10) = 90

Reorder the terms:
(-10 + x)(4x + -10) = 90

Reorder the terms:
(-10 + x)(-10 + 4x) = 90

Multiply (-10 + x) * (-10 + 4x)
(-10(-10 + 4x) + x(-10 + 4x)) = 90
((-10 * -10 + 4x * -10) + x(-10 + 4x)) = 90
((100 + -40x) + x(-10 + 4x)) = 90
(100 + -40x + (-10 * x + 4x * x)) = 90
(100 + -40x + (-10x + 4x2)) = 90

Combine like terms: -40x + -10x = -50x
(100 + -50x + 4x2) = 90

Solving
100 + -50x + 4x2 = 90

Solving for variable 'x'.

Reorder the terms:
100 + -90 + -50x + 4x2 = 90 + -90

Combine like terms: 100 + -90 = 10
10 + -50x + 4x2 = 90 + -90

Combine like terms: 90 + -90 = 0
10 + -50x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -25x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(5 + -25x + 2x2)' equal to zero and attempt to solve:

Simplifying
5 + -25x + 2x2 = 0

Solving
5 + -25x + 2x2 = 0

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

Divide each side by '2'.
2.5 + -12.5x + x2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + -12.5x + -2.5 + x2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + -12.5x + x2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + -12.5x + x2 = 0 + -2.5
-12.5x + x2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
-12.5x + x2 = -2.5

The x term is -12.5x.  Take half its coefficient (-6.25).
Square it (39.0625) and add it to both sides.

Add '39.0625' to each side of the equation.
-12.5x + 39.0625 + x2 = -2.5 + 39.0625

Reorder the terms:
39.0625 + -12.5x + x2 = -2.5 + 39.0625

Combine like terms: -2.5 + 39.0625 = 36.5625
39.0625 + -12.5x + x2 = 36.5625

Factor a perfect square on the left side:
(x + -6.25)(x + -6.25) = 36.5625

Calculate the square root of the right side: 6.046693311

Break this problem into two subproblems by setting 
(x + -6.25) equal to 6.046693311 and -6.046693311.

Subproblem 1
x + -6.25 = 6.046693311

Simplifying
x + -6.25 = 6.046693311

Reorder the terms:
-6.25 + x = 6.046693311

Solving
-6.25 + x = 6.046693311

Solving for variable 'x'.

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

Add '6.25' to each side of the equation.
-6.25 + 6.25 + x = 6.046693311 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + x = 6.046693311 + 6.25
x = 6.046693311 + 6.25

Combine like terms: 6.046693311 + 6.25 = 12.296693311
x = 12.296693311

Simplifying
x = 12.296693311

Subproblem 2
x + -6.25 = -6.046693311

Simplifying
x + -6.25 = -6.046693311

Reorder the terms:
-6.25 + x = -6.046693311

Solving
-6.25 + x = -6.046693311

Solving for variable 'x'.

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

Add '6.25' to each side of the equation.
-6.25 + 6.25 + x = -6.046693311 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + x = -6.046693311 + 6.25
x = -6.046693311 + 6.25

Combine like terms: -6.046693311 + 6.25 = 0.203306689
x = 0.203306689

Simplifying
x = 0.203306689

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.296693311, 0.203306689}
Solution
x = {12.296693311, 0.203306689}