6x(5x+4)=4

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


Simplifying
6x(5x + 4) = 4

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

Solving
24x + 30x2 = 4

Solving for variable 'x'.

Reorder the terms:
-4 + 24x + 30x2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + 24x + 30x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + 12x + 15x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-2 + 12x + 15x2)' equal to zero and attempt to solve:

Simplifying
-2 + 12x + 15x2 = 0

Solving
-2 + 12x + 15x2 = 0

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

Divide each side by '15'.
-0.1333333333 + 0.8x + x2 = 0

Move the constant term to the right:

Add '0.1333333333' to each side of the equation.
-0.1333333333 + 0.8x + 0.1333333333 + x2 = 0 + 0.1333333333

Reorder the terms:
-0.1333333333 + 0.1333333333 + 0.8x + x2 = 0 + 0.1333333333

Combine like terms: -0.1333333333 + 0.1333333333 = 0.0000000000
0.0000000000 + 0.8x + x2 = 0 + 0.1333333333
0.8x + x2 = 0 + 0.1333333333

Combine like terms: 0 + 0.1333333333 = 0.1333333333
0.8x + x2 = 0.1333333333

The x term is 0.8x.  Take half its coefficient (0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
0.8x + 0.16 + x2 = 0.1333333333 + 0.16

Reorder the terms:
0.16 + 0.8x + x2 = 0.1333333333 + 0.16

Combine like terms: 0.1333333333 + 0.16 = 0.2933333333
0.16 + 0.8x + x2 = 0.2933333333

Factor a perfect square on the left side:
(x + 0.4)(x + 0.4) = 0.2933333333

Calculate the square root of the right side: 0.54160256

Break this problem into two subproblems by setting 
(x + 0.4) equal to 0.54160256 and -0.54160256.


Subproblem 1
x + 0.4 = 0.54160256

Simplifying
x + 0.4 = 0.54160256

Reorder the terms:
0.4 + x = 0.54160256

Solving
0.4 + x = 0.54160256

Solving for variable 'x'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + x = 0.54160256 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + x = 0.54160256 + -0.4
x = 0.54160256 + -0.4

Combine like terms: 0.54160256 + -0.4 = 0.14160256
x = 0.14160256

Simplifying
x = 0.14160256


Subproblem 2
x + 0.4 = -0.54160256

Simplifying
x + 0.4 = -0.54160256

Reorder the terms:
0.4 + x = -0.54160256

Solving
0.4 + x = -0.54160256

Solving for variable 'x'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + x = -0.54160256 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + x = -0.54160256 + -0.4
x = -0.54160256 + -0.4

Combine like terms: -0.54160256 + -0.4 = -0.94160256
x = -0.94160256

Simplifying
x = -0.94160256


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.14160256, -0.94160256}
Solution
x = {0.14160256, -0.94160256}

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