x(3x+3)=210

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Solution for x(3x+3)=210 equation: 


Simplifying
x(3x + 3) = 210

Reorder the terms:
x(3 + 3x) = 210
(3 * x + 3x * x) = 210
(3x + 3x2) = 210

Solving
3x + 3x2 = 210

Solving for variable 'x'.

Reorder the terms:
-210 + 3x + 3x2 = 210 + -210

Combine like terms: 210 + -210 = 0
-210 + 3x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-70 + x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-70 + x + x2)' equal to zero and attempt to solve:

Simplifying
-70 + x + x2 = 0

Solving
-70 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '70' to each side of the equation.
-70 + x + 70 + x2 = 0 + 70

Reorder the terms:
-70 + 70 + x + x2 = 0 + 70

Combine like terms: -70 + 70 = 0
0 + x + x2 = 0 + 70
x + x2 = 0 + 70

Combine like terms: 0 + 70 = 70
x + x2 = 70

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.
x + 0.25 + x2 = 70 + 0.25

Reorder the terms:
0.25 + x + x2 = 70 + 0.25

Combine like terms: 70 + 0.25 = 70.25
0.25 + x + x2 = 70.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 70.25

Calculate the square root of the right side: 8.381527307

Break this problem into two subproblems by setting 
(x + 0.5) equal to 8.381527307 and -8.381527307.


Subproblem 1
x + 0.5 = 8.381527307

Simplifying
x + 0.5 = 8.381527307

Reorder the terms:
0.5 + x = 8.381527307

Solving
0.5 + x = 8.381527307

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 = 8.381527307 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 8.381527307 + -0.5
x = 8.381527307 + -0.5

Combine like terms: 8.381527307 + -0.5 = 7.881527307
x = 7.881527307

Simplifying
x = 7.881527307


Subproblem 2
x + 0.5 = -8.381527307

Simplifying
x + 0.5 = -8.381527307

Reorder the terms:
0.5 + x = -8.381527307

Solving
0.5 + x = -8.381527307

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 = -8.381527307 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -8.381527307 + -0.5
x = -8.381527307 + -0.5

Combine like terms: -8.381527307 + -0.5 = -8.881527307
x = -8.881527307

Simplifying
x = -8.881527307


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.881527307, -8.881527307}
Solution
x = {7.881527307, -8.881527307}

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