(x-10)(2x+21)=195

Solution for (x-10)(2x+21)=195 equation:

Simplifying
(x + -10)(2x + 21) = 195

Reorder the terms:
(-10 + x)(2x + 21) = 195

Reorder the terms:
(-10 + x)(21 + 2x) = 195

Multiply (-10 + x) * (21 + 2x)
(-10(21 + 2x) + x(21 + 2x)) = 195
((21 * -10 + 2x * -10) + x(21 + 2x)) = 195
((-210 + -20x) + x(21 + 2x)) = 195
(-210 + -20x + (21 * x + 2x * x)) = 195
(-210 + -20x + (21x + 2x2)) = 195

Combine like terms: -20x + 21x = 1x
(-210 + 1x + 2x2) = 195

Solving
-210 + 1x + 2x2 = 195

Solving for variable 'x'.

Reorder the terms:
-210 + -195 + 1x + 2x2 = 195 + -195

Combine like terms: -210 + -195 = -405
-405 + 1x + 2x2 = 195 + -195

Combine like terms: 195 + -195 = 0
-405 + 1x + 2x2 = 0

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

Divide each side by '2'.
-202.5 + 0.5x + x2 = 0

Move the constant term to the right:

Add '202.5' to each side of the equation.
-202.5 + 0.5x + 202.5 + x2 = 0 + 202.5

Reorder the terms:
-202.5 + 202.5 + 0.5x + x2 = 0 + 202.5

Combine like terms: -202.5 + 202.5 = 0.0
0.0 + 0.5x + x2 = 0 + 202.5
0.5x + x2 = 0 + 202.5

Combine like terms: 0 + 202.5 = 202.5
0.5x + x2 = 202.5

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 202.5 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 202.5 + 0.0625

Combine like terms: 202.5 + 0.0625 = 202.5625
0.0625 + 0.5x + x2 = 202.5625

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 202.5625

Calculate the square root of the right side: 14.232445327

Break this problem into two subproblems by setting 
(x + 0.25) equal to 14.232445327 and -14.232445327.

Subproblem 1
x + 0.25 = 14.232445327

Simplifying
x + 0.25 = 14.232445327

Reorder the terms:
0.25 + x = 14.232445327

Solving
0.25 + x = 14.232445327

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 14.232445327 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 14.232445327 + -0.25
x = 14.232445327 + -0.25

Combine like terms: 14.232445327 + -0.25 = 13.982445327
x = 13.982445327

Simplifying
x = 13.982445327

Subproblem 2
x + 0.25 = -14.232445327

Simplifying
x + 0.25 = -14.232445327

Reorder the terms:
0.25 + x = -14.232445327

Solving
0.25 + x = -14.232445327

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -14.232445327 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -14.232445327 + -0.25
x = -14.232445327 + -0.25

Combine like terms: -14.232445327 + -0.25 = -14.482445327
x = -14.482445327

Simplifying
x = -14.482445327

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.982445327, -14.482445327}