6x(5x+4)=3

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Solution for 6x(5x+4)=3 equation: 


Simplifying
6x(5x + 4) = 3

Reorder the terms:
6x(4 + 5x) = 3
(4 * 6x + 5x * 6x) = 3
(24x + 30x2) = 3

Solving
24x + 30x2 = 3

Solving for variable 'x'.

Reorder the terms:
-3 + 24x + 30x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 24x + 30x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + 8x + 10x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-1 + 8x + 10x2)' equal to zero and attempt to solve:

Simplifying
-1 + 8x + 10x2 = 0

Solving
-1 + 8x + 10x2 = 0

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

Divide each side by '10'.
-0.1 + 0.8x + x2 = 0.0

Move the constant term to the right:

Add '0.1' to each side of the equation.
-0.1 + 0.8x + 0.1 + x2 = 0.0 + 0.1

Reorder the terms:
-0.1 + 0.1 + 0.8x + x2 = 0.0 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + 0.8x + x2 = 0.0 + 0.1
0.8x + x2 = 0.0 + 0.1

Combine like terms: 0.0 + 0.1 = 0.1
0.8x + x2 = 0.1

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 = 0.1 + 0.16

Reorder the terms:
0.16 + 0.8x + x2 = 0.1 + 0.16

Combine like terms: 0.1 + 0.16 = 0.26
0.16 + 0.8x + x2 = 0.26

Factor a perfect square on the left side:
(x + 0.4)(x + 0.4) = 0.26

Calculate the square root of the right side: 0.509901951

Break this problem into two subproblems by setting 
(x + 0.4) equal to 0.509901951 and -0.509901951.


Subproblem 1
x + 0.4 = 0.509901951

Simplifying
x + 0.4 = 0.509901951

Reorder the terms:
0.4 + x = 0.509901951

Solving
0.4 + x = 0.509901951

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 = 0.509901951 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + x = 0.509901951 + -0.4
x = 0.509901951 + -0.4

Combine like terms: 0.509901951 + -0.4 = 0.109901951
x = 0.109901951

Simplifying
x = 0.109901951


Subproblem 2
x + 0.4 = -0.509901951

Simplifying
x + 0.4 = -0.509901951

Reorder the terms:
0.4 + x = -0.509901951

Solving
0.4 + x = -0.509901951

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 = -0.509901951 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + x = -0.509901951 + -0.4
x = -0.509901951 + -0.4

Combine like terms: -0.509901951 + -0.4 = -0.909901951
x = -0.909901951

Simplifying
x = -0.909901951


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.109901951, -0.909901951}
Solution
x = {0.109901951, -0.909901951}

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