4x(3x)+3x=75

Solution for 4x(3x)+3x=75 equation:

Simplifying
4x(3x) + 3x = 75

Remove parenthesis around (3x)
4x * 3x + 3x = 75

Reorder the terms for easier multiplication:
4 * 3x * x + 3x = 75

Multiply 4 * 3
12x * x + 3x = 75

Multiply x * x
12x2 + 3x = 75

Reorder the terms:
3x + 12x2 = 75

Solving
3x + 12x2 = 75

Solving for variable 'x'.

Reorder the terms:
-75 + 3x + 12x2 = 75 + -75

Combine like terms: 75 + -75 = 0
-75 + 3x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-25 + x + 4x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-25 + x + 4x2)' equal to zero and attempt to solve:

Simplifying
-25 + x + 4x2 = 0

Solving
-25 + x + 4x2 = 0

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

Divide each side by '4'.
-6.25 + 0.25x + x2 = 0

Move the constant term to the right:

Add '6.25' to each side of the equation.
-6.25 + 0.25x + 6.25 + x2 = 0 + 6.25

Reorder the terms:
-6.25 + 6.25 + 0.25x + x2 = 0 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + 0.25x + x2 = 0 + 6.25
0.25x + x2 = 0 + 6.25

Combine like terms: 0 + 6.25 = 6.25
0.25x + x2 = 6.25

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

Add '0.25' to each side of the equation.
0.25x + 0.25 + x2 = 6.25 + 0.25

Reorder the terms:
0.25 + 0.25x + x2 = 6.25 + 0.25

Combine like terms: 6.25 + 0.25 = 6.5
0.25 + 0.25x + x2 = 6.5

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 6.5

Calculate the square root of the right side: 2.549509757

Break this problem into two subproblems by setting 
(x + 0.5) equal to 2.549509757 and -2.549509757.

Subproblem 1
x + 0.5 = 2.549509757

Simplifying
x + 0.5 = 2.549509757

Reorder the terms:
0.5 + x = 2.549509757

Solving
0.5 + x = 2.549509757

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 2.549509757 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 2.549509757 + -0.5
x = 2.549509757 + -0.5

Combine like terms: 2.549509757 + -0.5 = 2.049509757
x = 2.049509757

Simplifying
x = 2.049509757

Subproblem 2
x + 0.5 = -2.549509757

Simplifying
x + 0.5 = -2.549509757

Reorder the terms:
0.5 + x = -2.549509757

Solving
0.5 + x = -2.549509757

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -2.549509757 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -2.549509757 + -0.5
x = -2.549509757 + -0.5

Combine like terms: -2.549509757 + -0.5 = -3.049509757
x = -3.049509757

Simplifying
x = -3.049509757

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.049509757, -3.049509757}
Solution
x = {2.049509757, -3.049509757}