3x*(10x+5)=3

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Solution for 3x*(10x+5)=3 equation: 


Simplifying
3x(10x + 5) = 3

Reorder the terms:
3x(5 + 10x) = 3
(5 * 3x + 10x * 3x) = 3
(15x + 30x2) = 3

Solving
15x + 30x2 = 3

Solving for variable 'x'.

Reorder the terms:
-3 + 15x + 30x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 15x + 30x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + 5x + 10x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-1 + 5x + 10x2)' equal to zero and attempt to solve:

Simplifying
-1 + 5x + 10x2 = 0

Solving
-1 + 5x + 10x2 = 0

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

Divide each side by '10'.
-0.1 + 0.5x + x2 = 0.0

Move the constant term to the right:

Add '0.1' to each side of the equation.
-0.1 + 0.5x + 0.1 + x2 = 0.0 + 0.1

Reorder the terms:
-0.1 + 0.1 + 0.5x + x2 = 0.0 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + 0.5x + x2 = 0.0 + 0.1
0.5x + x2 = 0.0 + 0.1

Combine like terms: 0.0 + 0.1 = 0.1
0.5x + x2 = 0.1

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 0.1 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 0.1 + 0.0625

Combine like terms: 0.1 + 0.0625 = 0.1625
0.0625 + 0.5x + x2 = 0.1625

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 0.1625

Calculate the square root of the right side: 0.403112887

Break this problem into two subproblems by setting 
(x + 0.25) equal to 0.403112887 and -0.403112887.


Subproblem 1
x + 0.25 = 0.403112887

Simplifying
x + 0.25 = 0.403112887

Reorder the terms:
0.25 + x = 0.403112887

Solving
0.25 + x = 0.403112887

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 0.403112887 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 0.403112887 + -0.25
x = 0.403112887 + -0.25

Combine like terms: 0.403112887 + -0.25 = 0.153112887
x = 0.153112887

Simplifying
x = 0.153112887


Subproblem 2
x + 0.25 = -0.403112887

Simplifying
x + 0.25 = -0.403112887

Reorder the terms:
0.25 + x = -0.403112887

Solving
0.25 + x = -0.403112887

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -0.403112887 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -0.403112887 + -0.25
x = -0.403112887 + -0.25

Combine like terms: -0.403112887 + -0.25 = -0.653112887
x = -0.653112887

Simplifying
x = -0.653112887


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.153112887, -0.653112887}
Solution
x = {0.153112887, -0.653112887}

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