6x(x+5)=-28

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Solution for 6x(x+5)=-28 equation: 


Simplifying
6x(x + 5) = -28

Reorder the terms:
6x(5 + x) = -28
(5 * 6x + x * 6x) = -28
(30x + 6x2) = -28

Solving
30x + 6x2 = -28

Solving for variable 'x'.

Reorder the terms:
28 + 30x + 6x2 = -28 + 28

Combine like terms: -28 + 28 = 0
28 + 30x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(14 + 15x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(14 + 15x + 3x2)' equal to zero and attempt to solve:

Simplifying
14 + 15x + 3x2 = 0

Solving
14 + 15x + 3x2 = 0

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

Divide each side by '3'.
4.666666667 + 5x + x2 = 0

Move the constant term to the right:

Add '-4.666666667' to each side of the equation.
4.666666667 + 5x + -4.666666667 + x2 = 0 + -4.666666667

Reorder the terms:
4.666666667 + -4.666666667 + 5x + x2 = 0 + -4.666666667

Combine like terms: 4.666666667 + -4.666666667 = 0.000000000
0.000000000 + 5x + x2 = 0 + -4.666666667
5x + x2 = 0 + -4.666666667

Combine like terms: 0 + -4.666666667 = -4.666666667
5x + x2 = -4.666666667

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 = -4.666666667 + 6.25

Reorder the terms:
6.25 + 5x + x2 = -4.666666667 + 6.25

Combine like terms: -4.666666667 + 6.25 = 1.583333333
6.25 + 5x + x2 = 1.583333333

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 1.583333333

Calculate the square root of the right side: 1.258305739

Break this problem into two subproblems by setting 
(x + 2.5) equal to 1.258305739 and -1.258305739.


Subproblem 1
x + 2.5 = 1.258305739

Simplifying
x + 2.5 = 1.258305739

Reorder the terms:
2.5 + x = 1.258305739

Solving
2.5 + x = 1.258305739

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 = 1.258305739 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 1.258305739 + -2.5
x = 1.258305739 + -2.5

Combine like terms: 1.258305739 + -2.5 = -1.241694261
x = -1.241694261

Simplifying
x = -1.241694261


Subproblem 2
x + 2.5 = -1.258305739

Simplifying
x + 2.5 = -1.258305739

Reorder the terms:
2.5 + x = -1.258305739

Solving
2.5 + x = -1.258305739

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 = -1.258305739 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -1.258305739 + -2.5
x = -1.258305739 + -2.5

Combine like terms: -1.258305739 + -2.5 = -3.758305739
x = -3.758305739

Simplifying
x = -3.758305739


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.241694261, -3.758305739}
Solution
x = {-1.241694261, -3.758305739}

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