(x)(x+3)(3)=150

Solution for (x)(x+3)(3)=150 equation:

Simplifying
(x)(x + 3)(3) = 150

Reorder the terms:
x(3 + x)(3) = 150

Reorder the terms for easier multiplication:
3x(3 + x) = 150
(3 * 3x + x * 3x) = 150
(9x + 3x2) = 150

Solving
9x + 3x2 = 150

Solving for variable 'x'.

Reorder the terms:
-150 + 9x + 3x2 = 150 + -150

Combine like terms: 150 + -150 = 0
-150 + 9x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-50 + 3x + x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-50 + 3x + x2)' equal to zero and attempt to solve:

Simplifying
-50 + 3x + x2 = 0

Solving
-50 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '50' to each side of the equation.
-50 + 3x + 50 + x2 = 0 + 50

Reorder the terms:
-50 + 50 + 3x + x2 = 0 + 50

Combine like terms: -50 + 50 = 0
0 + 3x + x2 = 0 + 50
3x + x2 = 0 + 50

Combine like terms: 0 + 50 = 50
3x + x2 = 50

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 = 50 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 50 + 2.25

Combine like terms: 50 + 2.25 = 52.25
2.25 + 3x + x2 = 52.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 52.25

Calculate the square root of the right side: 7.228416147

Break this problem into two subproblems by setting 
(x + 1.5) equal to 7.228416147 and -7.228416147.

Subproblem 1
x + 1.5 = 7.228416147

Simplifying
x + 1.5 = 7.228416147

Reorder the terms:
1.5 + x = 7.228416147

Solving
1.5 + x = 7.228416147

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 = 7.228416147 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 7.228416147 + -1.5
x = 7.228416147 + -1.5

Combine like terms: 7.228416147 + -1.5 = 5.728416147
x = 5.728416147

Simplifying
x = 5.728416147

Subproblem 2
x + 1.5 = -7.228416147

Simplifying
x + 1.5 = -7.228416147

Reorder the terms:
1.5 + x = -7.228416147

Solving
1.5 + x = -7.228416147

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 = -7.228416147 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -7.228416147 + -1.5
x = -7.228416147 + -1.5

Combine like terms: -7.228416147 + -1.5 = -8.728416147
x = -8.728416147

Simplifying
x = -8.728416147

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.728416147, -8.728416147}
Solution
x = {5.728416147, -8.728416147}