2x(6*5)5x=12x+3

Solution for 2x(6*5)5x=12x+3 equation:

Simplifying
2x(6 * 5) * 5x = 12x + 3

Multiply 6 * 5
2x(30) * 5x = 12x + 3

Reorder the terms for easier multiplication:
2 * 30 * 5x * x = 12x + 3

Multiply 2 * 30
60 * 5x * x = 12x + 3

Multiply 60 * 5
300x * x = 12x + 3

Multiply x * x
300x2 = 12x + 3

Reorder the terms:
300x2 = 3 + 12x

Solving
300x2 = 3 + 12x

Solving for variable 'x'.

Reorder the terms:
-3 + -12x + 300x2 = 3 + 12x + -3 + -12x

Reorder the terms:
-3 + -12x + 300x2 = 3 + -3 + 12x + -12x

Combine like terms: 3 + -3 = 0
-3 + -12x + 300x2 = 0 + 12x + -12x
-3 + -12x + 300x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
-3 + -12x + 300x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + -4x + 100x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-1 + -4x + 100x2)' equal to zero and attempt to solve:

Simplifying
-1 + -4x + 100x2 = 0

Solving
-1 + -4x + 100x2 = 0

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

Divide each side by '100'.
-0.01 + -0.04x + x2 = 0.00

Move the constant term to the right:

Add '0.01' to each side of the equation.
-0.01 + -0.04x + 0.01 + x2 = 0.00 + 0.01

Reorder the terms:
-0.01 + 0.01 + -0.04x + x2 = 0.00 + 0.01

Combine like terms: -0.01 + 0.01 = 0.00
0.00 + -0.04x + x2 = 0.00 + 0.01
-0.04x + x2 = 0.00 + 0.01

Combine like terms: 0.00 + 0.01 = 0.01
-0.04x + x2 = 0.01

The x term is -0.04x.  Take half its coefficient (-0.02).
Square it (0.0004) and add it to both sides.

Add '0.0004' to each side of the equation.
-0.04x + 0.0004 + x2 = 0.01 + 0.0004

Reorder the terms:
0.0004 + -0.04x + x2 = 0.01 + 0.0004

Combine like terms: 0.01 + 0.0004 = 0.0104
0.0004 + -0.04x + x2 = 0.0104

Factor a perfect square on the left side:
(x + -0.02)(x + -0.02) = 0.0104

Calculate the square root of the right side: 0.10198039

Break this problem into two subproblems by setting 
(x + -0.02) equal to 0.10198039 and -0.10198039.

Subproblem 1
x + -0.02 = 0.10198039

Simplifying
x + -0.02 = 0.10198039

Reorder the terms:
-0.02 + x = 0.10198039

Solving
-0.02 + x = 0.10198039

Solving for variable 'x'.

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

Add '0.02' to each side of the equation.
-0.02 + 0.02 + x = 0.10198039 + 0.02

Combine like terms: -0.02 + 0.02 = 0.00
0.00 + x = 0.10198039 + 0.02
x = 0.10198039 + 0.02

Combine like terms: 0.10198039 + 0.02 = 0.12198039
x = 0.12198039

Simplifying
x = 0.12198039

Subproblem 2
x + -0.02 = -0.10198039

Simplifying
x + -0.02 = -0.10198039

Reorder the terms:
-0.02 + x = -0.10198039

Solving
-0.02 + x = -0.10198039

Solving for variable 'x'.

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

Add '0.02' to each side of the equation.
-0.02 + 0.02 + x = -0.10198039 + 0.02

Combine like terms: -0.02 + 0.02 = 0.00
0.00 + x = -0.10198039 + 0.02
x = -0.10198039 + 0.02

Combine like terms: -0.10198039 + 0.02 = -0.08198039
x = -0.08198039

Simplifying
x = -0.08198039

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.12198039, -0.08198039}
Solution
x = {0.12198039, -0.08198039}