6x(4x+5)=13

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Solution for 6x(4x+5)=13 equation: 


Simplifying
6x(4x + 5) = 13

Reorder the terms:
6x(5 + 4x) = 13
(5 * 6x + 4x * 6x) = 13
(30x + 24x2) = 13

Solving
30x + 24x2 = 13

Solving for variable 'x'.

Reorder the terms:
-13 + 30x + 24x2 = 13 + -13

Combine like terms: 13 + -13 = 0
-13 + 30x + 24x2 = 0

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

Divide each side by '24'.
-0.5416666667 + 1.25x + x2 = 0

Move the constant term to the right:

Add '0.5416666667' to each side of the equation.
-0.5416666667 + 1.25x + 0.5416666667 + x2 = 0 + 0.5416666667

Reorder the terms:
-0.5416666667 + 0.5416666667 + 1.25x + x2 = 0 + 0.5416666667

Combine like terms: -0.5416666667 + 0.5416666667 = 0.0000000000
0.0000000000 + 1.25x + x2 = 0 + 0.5416666667
1.25x + x2 = 0 + 0.5416666667

Combine like terms: 0 + 0.5416666667 = 0.5416666667
1.25x + x2 = 0.5416666667

The x term is 1.25x.  Take half its coefficient (0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
1.25x + 0.390625 + x2 = 0.5416666667 + 0.390625

Reorder the terms:
0.390625 + 1.25x + x2 = 0.5416666667 + 0.390625

Combine like terms: 0.5416666667 + 0.390625 = 0.9322916667
0.390625 + 1.25x + x2 = 0.9322916667

Factor a perfect square on the left side:
(x + 0.625)(x + 0.625) = 0.9322916667

Calculate the square root of the right side: 0.965552519

Break this problem into two subproblems by setting 
(x + 0.625) equal to 0.965552519 and -0.965552519.


Subproblem 1
x + 0.625 = 0.965552519

Simplifying
x + 0.625 = 0.965552519

Reorder the terms:
0.625 + x = 0.965552519

Solving
0.625 + x = 0.965552519

Solving for variable 'x'.

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

Add '-0.625' to each side of the equation.
0.625 + -0.625 + x = 0.965552519 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + x = 0.965552519 + -0.625
x = 0.965552519 + -0.625

Combine like terms: 0.965552519 + -0.625 = 0.340552519
x = 0.340552519

Simplifying
x = 0.340552519


Subproblem 2
x + 0.625 = -0.965552519

Simplifying
x + 0.625 = -0.965552519

Reorder the terms:
0.625 + x = -0.965552519

Solving
0.625 + x = -0.965552519

Solving for variable 'x'.

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

Add '-0.625' to each side of the equation.
0.625 + -0.625 + x = -0.965552519 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + x = -0.965552519 + -0.625
x = -0.965552519 + -0.625

Combine like terms: -0.965552519 + -0.625 = -1.590552519
x = -1.590552519

Simplifying
x = -1.590552519


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.340552519, -1.590552519}

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