228=(2x+10)(3x)

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Solution for 228=(2x+10)(3x) equation: 


Simplifying
228 = (2x + 10)(3x)

Reorder the terms:
228 = (10 + 2x)(3x)

Remove parenthesis around (3x)
228 = (10 + 2x) * 3x

Reorder the terms for easier multiplication:
228 = 3x(10 + 2x)
228 = (10 * 3x + 2x * 3x)
228 = (30x + 6x2)

Solving
228 = 30x + 6x2

Solving for variable 'x'.

Reorder the terms:
228 + -30x + -6x2 = 30x + -30x + 6x2 + -6x2

Combine like terms: 30x + -30x = 0
228 + -30x + -6x2 = 0 + 6x2 + -6x2
228 + -30x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
228 + -30x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(38 + -5x + -1x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(38 + -5x + -1x2)' equal to zero and attempt to solve:

Simplifying
38 + -5x + -1x2 = 0

Solving
38 + -5x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-38 + 5x + x2 = 0

Move the constant term to the right:

Add '38' to each side of the equation.
-38 + 5x + 38 + x2 = 0 + 38

Reorder the terms:
-38 + 38 + 5x + x2 = 0 + 38

Combine like terms: -38 + 38 = 0
0 + 5x + x2 = 0 + 38
5x + x2 = 0 + 38

Combine like terms: 0 + 38 = 38
5x + x2 = 38

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 38 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 38 + 6.25

Combine like terms: 38 + 6.25 = 44.25
6.25 + 5x + x2 = 44.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 44.25

Calculate the square root of the right side: 6.652067348

Break this problem into two subproblems by setting 
(x + 2.5) equal to 6.652067348 and -6.652067348.


Subproblem 1
x + 2.5 = 6.652067348

Simplifying
x + 2.5 = 6.652067348

Reorder the terms:
2.5 + x = 6.652067348

Solving
2.5 + x = 6.652067348

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 6.652067348 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 6.652067348 + -2.5
x = 6.652067348 + -2.5

Combine like terms: 6.652067348 + -2.5 = 4.152067348
x = 4.152067348

Simplifying
x = 4.152067348


Subproblem 2
x + 2.5 = -6.652067348

Simplifying
x + 2.5 = -6.652067348

Reorder the terms:
2.5 + x = -6.652067348

Solving
2.5 + x = -6.652067348

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -6.652067348 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -6.652067348 + -2.5
x = -6.652067348 + -2.5

Combine like terms: -6.652067348 + -2.5 = -9.152067348
x = -9.152067348

Simplifying
x = -9.152067348


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.152067348, -9.152067348}
Solution
x = {4.152067348, -9.152067348}

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