3(x+3)4x=25

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Solution for 3(x+3)4x=25 equation: 


Simplifying
3(x + 3) * 4x = 25

Reorder the terms:
3(3 + x) * 4x = 25

Reorder the terms for easier multiplication:
3 * 4x(3 + x) = 25

Multiply 3 * 4
12x(3 + x) = 25
(3 * 12x + x * 12x) = 25
(36x + 12x2) = 25

Solving
36x + 12x2 = 25

Solving for variable 'x'.

Reorder the terms:
-25 + 36x + 12x2 = 25 + -25

Combine like terms: 25 + -25 = 0
-25 + 36x + 12x2 = 0

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

Divide each side by '12'.
-2.083333333 + 3x + x2 = 0

Move the constant term to the right:

Add '2.083333333' to each side of the equation.
-2.083333333 + 3x + 2.083333333 + x2 = 0 + 2.083333333

Reorder the terms:
-2.083333333 + 2.083333333 + 3x + x2 = 0 + 2.083333333

Combine like terms: -2.083333333 + 2.083333333 = 0.000000000
0.000000000 + 3x + x2 = 0 + 2.083333333
3x + x2 = 0 + 2.083333333

Combine like terms: 0 + 2.083333333 = 2.083333333
3x + x2 = 2.083333333

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 2.083333333 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 2.083333333 + 2.25

Combine like terms: 2.083333333 + 2.25 = 4.333333333
2.25 + 3x + x2 = 4.333333333

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 4.333333333

Calculate the square root of the right side: 2.081665999

Break this problem into two subproblems by setting 
(x + 1.5) equal to 2.081665999 and -2.081665999.


Subproblem 1
x + 1.5 = 2.081665999

Simplifying
x + 1.5 = 2.081665999

Reorder the terms:
1.5 + x = 2.081665999

Solving
1.5 + x = 2.081665999

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 2.081665999 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 2.081665999 + -1.5
x = 2.081665999 + -1.5

Combine like terms: 2.081665999 + -1.5 = 0.581665999
x = 0.581665999

Simplifying
x = 0.581665999


Subproblem 2
x + 1.5 = -2.081665999

Simplifying
x + 1.5 = -2.081665999

Reorder the terms:
1.5 + x = -2.081665999

Solving
1.5 + x = -2.081665999

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -2.081665999 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -2.081665999 + -1.5
x = -2.081665999 + -1.5

Combine like terms: -2.081665999 + -1.5 = -3.581665999
x = -3.581665999

Simplifying
x = -3.581665999


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.581665999, -3.581665999}

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