280=x(2x+6)

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Solution for 280=x(2x+6) equation: 


Simplifying
280 = x(2x + 6)

Reorder the terms:
280 = x(6 + 2x)
280 = (6 * x + 2x * x)
280 = (6x + 2x2)

Solving
280 = 6x + 2x2

Solving for variable 'x'.

Reorder the terms:
280 + -6x + -2x2 = 6x + -6x + 2x2 + -2x2

Combine like terms: 6x + -6x = 0
280 + -6x + -2x2 = 0 + 2x2 + -2x2
280 + -6x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
280 + -6x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(140 + -3x + -1x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(140 + -3x + -1x2)' equal to zero and attempt to solve:

Simplifying
140 + -3x + -1x2 = 0

Solving
140 + -3x + -1x2 = 0

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

Divide each side by '-1'.
-140 + 3x + x2 = 0

Move the constant term to the right:

Add '140' to each side of the equation.
-140 + 3x + 140 + x2 = 0 + 140

Reorder the terms:
-140 + 140 + 3x + x2 = 0 + 140

Combine like terms: -140 + 140 = 0
0 + 3x + x2 = 0 + 140
3x + x2 = 0 + 140

Combine like terms: 0 + 140 = 140
3x + x2 = 140

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 = 140 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 140 + 2.25

Combine like terms: 140 + 2.25 = 142.25
2.25 + 3x + x2 = 142.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 142.25

Calculate the square root of the right side: 11.926860442

Break this problem into two subproblems by setting 
(x + 1.5) equal to 11.926860442 and -11.926860442.


Subproblem 1
x + 1.5 = 11.926860442

Simplifying
x + 1.5 = 11.926860442

Reorder the terms:
1.5 + x = 11.926860442

Solving
1.5 + x = 11.926860442

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 = 11.926860442 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 11.926860442 + -1.5
x = 11.926860442 + -1.5

Combine like terms: 11.926860442 + -1.5 = 10.426860442
x = 10.426860442

Simplifying
x = 10.426860442


Subproblem 2
x + 1.5 = -11.926860442

Simplifying
x + 1.5 = -11.926860442

Reorder the terms:
1.5 + x = -11.926860442

Solving
1.5 + x = -11.926860442

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 = -11.926860442 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -11.926860442 + -1.5
x = -11.926860442 + -1.5

Combine like terms: -11.926860442 + -1.5 = -13.426860442
x = -13.426860442

Simplifying
x = -13.426860442


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.426860442, -13.426860442}
Solution
x = {10.426860442, -13.426860442}

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