3x(2x+5)=360

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Solution for 3x(2x+5)=360 equation: 


Simplifying
3x(2x + 5) = 360

Reorder the terms:
3x(5 + 2x) = 360
(5 * 3x + 2x * 3x) = 360
(15x + 6x2) = 360

Solving
15x + 6x2 = 360

Solving for variable 'x'.

Reorder the terms:
-360 + 15x + 6x2 = 360 + -360

Combine like terms: 360 + -360 = 0
-360 + 15x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-120 + 5x + 2x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-120 + 5x + 2x2)' equal to zero and attempt to solve:

Simplifying
-120 + 5x + 2x2 = 0

Solving
-120 + 5x + 2x2 = 0

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

Divide each side by '2'.
-60 + 2.5x + x2 = 0

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + 2.5x + 60 + x2 = 0 + 60

Reorder the terms:
-60 + 60 + 2.5x + x2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + 2.5x + x2 = 0 + 60
2.5x + x2 = 0 + 60

Combine like terms: 0 + 60 = 60
2.5x + x2 = 60

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 60 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 60 + 1.5625

Combine like terms: 60 + 1.5625 = 61.5625
1.5625 + 2.5x + x2 = 61.5625

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 61.5625

Calculate the square root of the right side: 7.846177413

Break this problem into two subproblems by setting 
(x + 1.25) equal to 7.846177413 and -7.846177413.


Subproblem 1
x + 1.25 = 7.846177413

Simplifying
x + 1.25 = 7.846177413

Reorder the terms:
1.25 + x = 7.846177413

Solving
1.25 + x = 7.846177413

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = 7.846177413 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = 7.846177413 + -1.25
x = 7.846177413 + -1.25

Combine like terms: 7.846177413 + -1.25 = 6.596177413
x = 6.596177413

Simplifying
x = 6.596177413


Subproblem 2
x + 1.25 = -7.846177413

Simplifying
x + 1.25 = -7.846177413

Reorder the terms:
1.25 + x = -7.846177413

Solving
1.25 + x = -7.846177413

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = -7.846177413 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = -7.846177413 + -1.25
x = -7.846177413 + -1.25

Combine like terms: -7.846177413 + -1.25 = -9.096177413
x = -9.096177413

Simplifying
x = -9.096177413


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.596177413, -9.096177413}
Solution
x = {6.596177413, -9.096177413}

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