x(2x+30)=204

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Solution for x(2x+30)=204 equation: 


Simplifying
x(2x + 30) = 204

Reorder the terms:
x(30 + 2x) = 204
(30 * x + 2x * x) = 204
(30x + 2x2) = 204

Solving
30x + 2x2 = 204

Solving for variable 'x'.

Reorder the terms:
-204 + 30x + 2x2 = 204 + -204

Combine like terms: 204 + -204 = 0
-204 + 30x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-102 + 15x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-102 + 15x + x2)' equal to zero and attempt to solve:

Simplifying
-102 + 15x + x2 = 0

Solving
-102 + 15x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '102' to each side of the equation.
-102 + 15x + 102 + x2 = 0 + 102

Reorder the terms:
-102 + 102 + 15x + x2 = 0 + 102

Combine like terms: -102 + 102 = 0
0 + 15x + x2 = 0 + 102
15x + x2 = 0 + 102

Combine like terms: 0 + 102 = 102
15x + x2 = 102

The x term is 15x.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15x + 56.25 + x2 = 102 + 56.25

Reorder the terms:
56.25 + 15x + x2 = 102 + 56.25

Combine like terms: 102 + 56.25 = 158.25
56.25 + 15x + x2 = 158.25

Factor a perfect square on the left side:
(x + 7.5)(x + 7.5) = 158.25

Calculate the square root of the right side: 12.579745625

Break this problem into two subproblems by setting 
(x + 7.5) equal to 12.579745625 and -12.579745625.


Subproblem 1
x + 7.5 = 12.579745625

Simplifying
x + 7.5 = 12.579745625

Reorder the terms:
7.5 + x = 12.579745625

Solving
7.5 + x = 12.579745625

Solving for variable 'x'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + x = 12.579745625 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = 12.579745625 + -7.5
x = 12.579745625 + -7.5

Combine like terms: 12.579745625 + -7.5 = 5.079745625
x = 5.079745625

Simplifying
x = 5.079745625


Subproblem 2
x + 7.5 = -12.579745625

Simplifying
x + 7.5 = -12.579745625

Reorder the terms:
7.5 + x = -12.579745625

Solving
7.5 + x = -12.579745625

Solving for variable 'x'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + x = -12.579745625 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = -12.579745625 + -7.5
x = -12.579745625 + -7.5

Combine like terms: -12.579745625 + -7.5 = -20.079745625
x = -20.079745625

Simplifying
x = -20.079745625


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.079745625, -20.079745625}
Solution
x = {5.079745625, -20.079745625}

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