3X(X+1)+X=2X(X+10)+5(X-10)-27

Solution for 3X(X+1)+X=2X(X+10)+5(X-10)-27 equation:

Simplifying
3X(X + 1) + X = 2X(X + 10) + 5(X + -10) + -27

Reorder the terms:
3X(1 + X) + X = 2X(X + 10) + 5(X + -10) + -27
(1 * 3X + X * 3X) + X = 2X(X + 10) + 5(X + -10) + -27
(3X + 3X2) + X = 2X(X + 10) + 5(X + -10) + -27

Reorder the terms:
3X + X + 3X2 = 2X(X + 10) + 5(X + -10) + -27

Combine like terms: 3X + X = 4X
4X + 3X2 = 2X(X + 10) + 5(X + -10) + -27

Reorder the terms:
4X + 3X2 = 2X(10 + X) + 5(X + -10) + -27
4X + 3X2 = (10 * 2X + X * 2X) + 5(X + -10) + -27
4X + 3X2 = (20X + 2X2) + 5(X + -10) + -27

Reorder the terms:
4X + 3X2 = 20X + 2X2 + 5(-10 + X) + -27
4X + 3X2 = 20X + 2X2 + (-10 * 5 + X * 5) + -27
4X + 3X2 = 20X + 2X2 + (-50 + 5X) + -27

Reorder the terms:
4X + 3X2 = -50 + -27 + 20X + 5X + 2X2

Combine like terms: -50 + -27 = -77
4X + 3X2 = -77 + 20X + 5X + 2X2

Combine like terms: 20X + 5X = 25X
4X + 3X2 = -77 + 25X + 2X2

Solving
4X + 3X2 = -77 + 25X + 2X2

Solving for variable 'X'.

Reorder the terms:
77 + 4X + -25X + 3X2 + -2X2 = -77 + 25X + 2X2 + 77 + -25X + -2X2

Combine like terms: 4X + -25X = -21X
77 + -21X + 3X2 + -2X2 = -77 + 25X + 2X2 + 77 + -25X + -2X2

Combine like terms: 3X2 + -2X2 = 1X2
77 + -21X + 1X2 = -77 + 25X + 2X2 + 77 + -25X + -2X2

Reorder the terms:
77 + -21X + 1X2 = -77 + 77 + 25X + -25X + 2X2 + -2X2

Combine like terms: -77 + 77 = 0
77 + -21X + 1X2 = 0 + 25X + -25X + 2X2 + -2X2
77 + -21X + 1X2 = 25X + -25X + 2X2 + -2X2

Combine like terms: 25X + -25X = 0
77 + -21X + 1X2 = 0 + 2X2 + -2X2
77 + -21X + 1X2 = 2X2 + -2X2

Combine like terms: 2X2 + -2X2 = 0
77 + -21X + 1X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-77' to each side of the equation.
77 + -21X + -77 + X2 = 0 + -77

Reorder the terms:
77 + -77 + -21X + X2 = 0 + -77

Combine like terms: 77 + -77 = 0
0 + -21X + X2 = 0 + -77
-21X + X2 = 0 + -77

Combine like terms: 0 + -77 = -77
-21X + X2 = -77

The X term is -21X.  Take half its coefficient (-10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
-21X + 110.25 + X2 = -77 + 110.25

Reorder the terms:
110.25 + -21X + X2 = -77 + 110.25

Combine like terms: -77 + 110.25 = 33.25
110.25 + -21X + X2 = 33.25

Factor a perfect square on the left side:
(X + -10.5)(X + -10.5) = 33.25

Calculate the square root of the right side: 5.766281297

Break this problem into two subproblems by setting 
(X + -10.5) equal to 5.766281297 and -5.766281297.

Subproblem 1
X + -10.5 = 5.766281297

Simplifying
X + -10.5 = 5.766281297

Reorder the terms:
-10.5 + X = 5.766281297

Solving
-10.5 + X = 5.766281297

Solving for variable 'X'.

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

Add '10.5' to each side of the equation.
-10.5 + 10.5 + X = 5.766281297 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + X = 5.766281297 + 10.5
X = 5.766281297 + 10.5

Combine like terms: 5.766281297 + 10.5 = 16.266281297
X = 16.266281297

Simplifying
X = 16.266281297

Subproblem 2
X + -10.5 = -5.766281297

Simplifying
X + -10.5 = -5.766281297

Reorder the terms:
-10.5 + X = -5.766281297

Solving
-10.5 + X = -5.766281297

Solving for variable 'X'.

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

Add '10.5' to each side of the equation.
-10.5 + 10.5 + X = -5.766281297 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + X = -5.766281297 + 10.5
X = -5.766281297 + 10.5

Combine like terms: -5.766281297 + 10.5 = 4.733718703
X = 4.733718703

Simplifying
X = 4.733718703

Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {16.266281297, 4.733718703}