3(x+5)4x=40

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Solution for 3(x+5)4x=40 equation: 


Simplifying
3(x + 5) * 4x = 40

Reorder the terms:
3(5 + x) * 4x = 40

Reorder the terms for easier multiplication:
3 * 4x(5 + x) = 40

Multiply 3 * 4
12x(5 + x) = 40
(5 * 12x + x * 12x) = 40
(60x + 12x2) = 40

Solving
60x + 12x2 = 40

Solving for variable 'x'.

Reorder the terms:
-40 + 60x + 12x2 = 40 + -40

Combine like terms: 40 + -40 = 0
-40 + 60x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-10 + 15x + 3x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-10 + 15x + 3x2)' equal to zero and attempt to solve:

Simplifying
-10 + 15x + 3x2 = 0

Solving
-10 + 15x + 3x2 = 0

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

Divide each side by '3'.
-3.333333333 + 5x + x2 = 0

Move the constant term to the right:

Add '3.333333333' to each side of the equation.
-3.333333333 + 5x + 3.333333333 + x2 = 0 + 3.333333333

Reorder the terms:
-3.333333333 + 3.333333333 + 5x + x2 = 0 + 3.333333333

Combine like terms: -3.333333333 + 3.333333333 = 0.000000000
0.000000000 + 5x + x2 = 0 + 3.333333333
5x + x2 = 0 + 3.333333333

Combine like terms: 0 + 3.333333333 = 3.333333333
5x + x2 = 3.333333333

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 3.333333333 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 3.333333333 + 6.25

Combine like terms: 3.333333333 + 6.25 = 9.583333333
6.25 + 5x + x2 = 9.583333333

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 9.583333333

Calculate the square root of the right side: 3.095695937

Break this problem into two subproblems by setting 
(x + 2.5) equal to 3.095695937 and -3.095695937.


Subproblem 1
x + 2.5 = 3.095695937

Simplifying
x + 2.5 = 3.095695937

Reorder the terms:
2.5 + x = 3.095695937

Solving
2.5 + x = 3.095695937

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 3.095695937 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 3.095695937 + -2.5
x = 3.095695937 + -2.5

Combine like terms: 3.095695937 + -2.5 = 0.595695937
x = 0.595695937

Simplifying
x = 0.595695937


Subproblem 2
x + 2.5 = -3.095695937

Simplifying
x + 2.5 = -3.095695937

Reorder the terms:
2.5 + x = -3.095695937

Solving
2.5 + x = -3.095695937

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -3.095695937 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -3.095695937 + -2.5
x = -3.095695937 + -2.5

Combine like terms: -3.095695937 + -2.5 = -5.595695937
x = -5.595695937

Simplifying
x = -5.595695937


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.595695937, -5.595695937}
Solution
x = {0.595695937, -5.595695937}

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