3x*4(x+10)=620

Solution for 3x*4(x+10)=620 equation:

Simplifying
3x * 4(x + 10) = 620

Reorder the terms:
3x * 4(10 + x) = 620

Reorder the terms for easier multiplication:
3 * 4x(10 + x) = 620

Multiply 3 * 4
12x(10 + x) = 620
(10 * 12x + x * 12x) = 620
(120x + 12x2) = 620

Solving
120x + 12x2 = 620

Solving for variable 'x'.

Reorder the terms:
-620 + 120x + 12x2 = 620 + -620

Combine like terms: 620 + -620 = 0
-620 + 120x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-155 + 30x + 3x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-155 + 30x + 3x2)' equal to zero and attempt to solve:

Simplifying
-155 + 30x + 3x2 = 0

Solving
-155 + 30x + 3x2 = 0

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

Divide each side by '3'.
-51.66666667 + 10x + x2 = 0

Move the constant term to the right:

Add '51.66666667' to each side of the equation.
-51.66666667 + 10x + 51.66666667 + x2 = 0 + 51.66666667

Reorder the terms:
-51.66666667 + 51.66666667 + 10x + x2 = 0 + 51.66666667

Combine like terms: -51.66666667 + 51.66666667 = 0.00000000
0.00000000 + 10x + x2 = 0 + 51.66666667
10x + x2 = 0 + 51.66666667

Combine like terms: 0 + 51.66666667 = 51.66666667
10x + x2 = 51.66666667

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = 51.66666667 + 25

Reorder the terms:
25 + 10x + x2 = 51.66666667 + 25

Combine like terms: 51.66666667 + 25 = 76.66666667
25 + 10x + x2 = 76.66666667

Factor a perfect square on the left side:
(x + 5)(x + 5) = 76.66666667

Calculate the square root of the right side: 8.755950358

Break this problem into two subproblems by setting 
(x + 5) equal to 8.755950358 and -8.755950358.

Subproblem 1
x + 5 = 8.755950358

Simplifying
x + 5 = 8.755950358

Reorder the terms:
5 + x = 8.755950358

Solving
5 + x = 8.755950358

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = 8.755950358 + -5

Combine like terms: 5 + -5 = 0
0 + x = 8.755950358 + -5
x = 8.755950358 + -5

Combine like terms: 8.755950358 + -5 = 3.755950358
x = 3.755950358

Simplifying
x = 3.755950358

Subproblem 2
x + 5 = -8.755950358

Simplifying
x + 5 = -8.755950358

Reorder the terms:
5 + x = -8.755950358

Solving
5 + x = -8.755950358

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = -8.755950358 + -5

Combine like terms: 5 + -5 = 0
0 + x = -8.755950358 + -5
x = -8.755950358 + -5

Combine like terms: -8.755950358 + -5 = -13.755950358
x = -13.755950358

Simplifying
x = -13.755950358

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.755950358, -13.755950358}
Solution
x = {3.755950358, -13.755950358}