x^2+15x^2+16=24x+26x^2+2x

Solution for x^2+15x^2+16=24x+26x^2+2x equation:

Simplifying
x2 + 15x2 + 16 = 24x + 26x2 + 2x

Reorder the terms:
16 + x2 + 15x2 = 24x + 26x2 + 2x

Combine like terms: x2 + 15x2 = 16x2
16 + 16x2 = 24x + 26x2 + 2x

Reorder the terms:
16 + 16x2 = 24x + 2x + 26x2

Combine like terms: 24x + 2x = 26x
16 + 16x2 = 26x + 26x2

Solving
16 + 16x2 = 26x + 26x2

Solving for variable 'x'.

Reorder the terms:
16 + -26x + 16x2 + -26x2 = 26x + 26x2 + -26x + -26x2

Combine like terms: 16x2 + -26x2 = -10x2
16 + -26x + -10x2 = 26x + 26x2 + -26x + -26x2

Reorder the terms:
16 + -26x + -10x2 = 26x + -26x + 26x2 + -26x2

Combine like terms: 26x + -26x = 0
16 + -26x + -10x2 = 0 + 26x2 + -26x2
16 + -26x + -10x2 = 26x2 + -26x2

Combine like terms: 26x2 + -26x2 = 0
16 + -26x + -10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + -13x + -5x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(8 + -13x + -5x2)' equal to zero and attempt to solve:

Simplifying
8 + -13x + -5x2 = 0

Solving
8 + -13x + -5x2 = 0

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

Divide each side by '-5'.
-1.6 + 2.6x + x2 = 0

Move the constant term to the right:

Add '1.6' to each side of the equation.
-1.6 + 2.6x + 1.6 + x2 = 0 + 1.6

Reorder the terms:
-1.6 + 1.6 + 2.6x + x2 = 0 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + 2.6x + x2 = 0 + 1.6
2.6x + x2 = 0 + 1.6

Combine like terms: 0 + 1.6 = 1.6
2.6x + x2 = 1.6

The x term is 2.6x.  Take half its coefficient (1.3).
Square it (1.69) and add it to both sides.

Add '1.69' to each side of the equation.
2.6x + 1.69 + x2 = 1.6 + 1.69

Reorder the terms:
1.69 + 2.6x + x2 = 1.6 + 1.69

Combine like terms: 1.6 + 1.69 = 3.29
1.69 + 2.6x + x2 = 3.29

Factor a perfect square on the left side:
(x + 1.3)(x + 1.3) = 3.29

Calculate the square root of the right side: 1.813835715

Break this problem into two subproblems by setting 
(x + 1.3) equal to 1.813835715 and -1.813835715.

Subproblem 1
x + 1.3 = 1.813835715

Simplifying
x + 1.3 = 1.813835715

Reorder the terms:
1.3 + x = 1.813835715

Solving
1.3 + x = 1.813835715

Solving for variable 'x'.

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

Add '-1.3' to each side of the equation.
1.3 + -1.3 + x = 1.813835715 + -1.3

Combine like terms: 1.3 + -1.3 = 0.0
0.0 + x = 1.813835715 + -1.3
x = 1.813835715 + -1.3

Combine like terms: 1.813835715 + -1.3 = 0.513835715
x = 0.513835715

Simplifying
x = 0.513835715

Subproblem 2
x + 1.3 = -1.813835715

Simplifying
x + 1.3 = -1.813835715

Reorder the terms:
1.3 + x = -1.813835715

Solving
1.3 + x = -1.813835715

Solving for variable 'x'.

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

Add '-1.3' to each side of the equation.
1.3 + -1.3 + x = -1.813835715 + -1.3

Combine like terms: 1.3 + -1.3 = 0.0
0.0 + x = -1.813835715 + -1.3
x = -1.813835715 + -1.3

Combine like terms: -1.813835715 + -1.3 = -3.113835715
x = -3.113835715

Simplifying
x = -3.113835715

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.513835715, -3.113835715}
Solution
x = {0.513835715, -3.113835715}