5x(2x-13)=15

Solution for 5x(2x-13)=15 equation:

Simplifying
5x(2x + -13) = 15

Reorder the terms:
5x(-13 + 2x) = 15
(-13 * 5x + 2x * 5x) = 15
(-65x + 10x2) = 15

Solving
-65x + 10x2 = 15

Solving for variable 'x'.

Reorder the terms:
-15 + -65x + 10x2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + -65x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-3 + -13x + 2x2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-3 + -13x + 2x2)' equal to zero and attempt to solve:

Simplifying
-3 + -13x + 2x2 = 0

Solving
-3 + -13x + 2x2 = 0

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

Divide each side by '2'.
-1.5 + -6.5x + x2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + -6.5x + 1.5 + x2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + -6.5x + x2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + -6.5x + x2 = 0 + 1.5
-6.5x + x2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
-6.5x + x2 = 1.5

The x term is -6.5x.  Take half its coefficient (-3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
-6.5x + 10.5625 + x2 = 1.5 + 10.5625

Reorder the terms:
10.5625 + -6.5x + x2 = 1.5 + 10.5625

Combine like terms: 1.5 + 10.5625 = 12.0625
10.5625 + -6.5x + x2 = 12.0625

Factor a perfect square on the left side:
(x + -3.25)(x + -3.25) = 12.0625

Calculate the square root of the right side: 3.473110997

Break this problem into two subproblems by setting 
(x + -3.25) equal to 3.473110997 and -3.473110997.

Subproblem 1
x + -3.25 = 3.473110997

Simplifying
x + -3.25 = 3.473110997

Reorder the terms:
-3.25 + x = 3.473110997

Solving
-3.25 + x = 3.473110997

Solving for variable 'x'.

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

Add '3.25' to each side of the equation.
-3.25 + 3.25 + x = 3.473110997 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + x = 3.473110997 + 3.25
x = 3.473110997 + 3.25

Combine like terms: 3.473110997 + 3.25 = 6.723110997
x = 6.723110997

Simplifying
x = 6.723110997

Subproblem 2
x + -3.25 = -3.473110997

Simplifying
x + -3.25 = -3.473110997

Reorder the terms:
-3.25 + x = -3.473110997

Solving
-3.25 + x = -3.473110997

Solving for variable 'x'.

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

Add '3.25' to each side of the equation.
-3.25 + 3.25 + x = -3.473110997 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + x = -3.473110997 + 3.25
x = -3.473110997 + 3.25

Combine like terms: -3.473110997 + 3.25 = -0.223110997
x = -0.223110997

Simplifying
x = -0.223110997

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.723110997, -0.223110997}
Solution
x = {6.723110997, -0.223110997}