6x(x+2)=292

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Solution for 6x(x+2)=292 equation: 


Simplifying
6x(x + 2) = 292

Reorder the terms:
6x(2 + x) = 292
(2 * 6x + x * 6x) = 292
(12x + 6x2) = 292

Solving
12x + 6x2 = 292

Solving for variable 'x'.

Reorder the terms:
-292 + 12x + 6x2 = 292 + -292

Combine like terms: 292 + -292 = 0
-292 + 12x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-146 + 6x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-146 + 6x + 3x2)' equal to zero and attempt to solve:

Simplifying
-146 + 6x + 3x2 = 0

Solving
-146 + 6x + 3x2 = 0

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

Divide each side by '3'.
-48.66666667 + 2x + x2 = 0

Move the constant term to the right:

Add '48.66666667' to each side of the equation.
-48.66666667 + 2x + 48.66666667 + x2 = 0 + 48.66666667

Reorder the terms:
-48.66666667 + 48.66666667 + 2x + x2 = 0 + 48.66666667

Combine like terms: -48.66666667 + 48.66666667 = 0.00000000
0.00000000 + 2x + x2 = 0 + 48.66666667
2x + x2 = 0 + 48.66666667

Combine like terms: 0 + 48.66666667 = 48.66666667
2x + x2 = 48.66666667

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 48.66666667 + 1

Reorder the terms:
1 + 2x + x2 = 48.66666667 + 1

Combine like terms: 48.66666667 + 1 = 49.66666667
1 + 2x + x2 = 49.66666667

Factor a perfect square on the left side:
(x + 1)(x + 1) = 49.66666667

Calculate the square root of the right side: 7.047458171

Break this problem into two subproblems by setting 
(x + 1) equal to 7.047458171 and -7.047458171.


Subproblem 1
x + 1 = 7.047458171

Simplifying
x + 1 = 7.047458171

Reorder the terms:
1 + x = 7.047458171

Solving
1 + x = 7.047458171

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 7.047458171 + -1

Combine like terms: 1 + -1 = 0
0 + x = 7.047458171 + -1
x = 7.047458171 + -1

Combine like terms: 7.047458171 + -1 = 6.047458171
x = 6.047458171

Simplifying
x = 6.047458171


Subproblem 2
x + 1 = -7.047458171

Simplifying
x + 1 = -7.047458171

Reorder the terms:
1 + x = -7.047458171

Solving
1 + x = -7.047458171

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -7.047458171 + -1

Combine like terms: 1 + -1 = 0
0 + x = -7.047458171 + -1
x = -7.047458171 + -1

Combine like terms: -7.047458171 + -1 = -8.047458171
x = -8.047458171

Simplifying
x = -8.047458171


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.047458171, -8.047458171}
Solution
x = {6.047458171, -8.047458171}

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