6x(5x+2)=180

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Solution for 6x(5x+2)=180 equation: 


Simplifying
6x(5x + 2) = 180

Reorder the terms:
6x(2 + 5x) = 180
(2 * 6x + 5x * 6x) = 180
(12x + 30x2) = 180

Solving
12x + 30x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 12x + 30x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 12x + 30x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-30 + 2x + 5x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-30 + 2x + 5x2)' equal to zero and attempt to solve:

Simplifying
-30 + 2x + 5x2 = 0

Solving
-30 + 2x + 5x2 = 0

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

Divide each side by '5'.
-6 + 0.4x + x2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 0.4x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + 0.4x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 0.4x + x2 = 0 + 6
0.4x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
0.4x + x2 = 6

The x term is 0.4x.  Take half its coefficient (0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
0.4x + 0.04 + x2 = 6 + 0.04

Reorder the terms:
0.04 + 0.4x + x2 = 6 + 0.04

Combine like terms: 6 + 0.04 = 6.04
0.04 + 0.4x + x2 = 6.04

Factor a perfect square on the left side:
(x + 0.2)(x + 0.2) = 6.04

Calculate the square root of the right side: 2.457641145

Break this problem into two subproblems by setting 
(x + 0.2) equal to 2.457641145 and -2.457641145.


Subproblem 1
x + 0.2 = 2.457641145

Simplifying
x + 0.2 = 2.457641145

Reorder the terms:
0.2 + x = 2.457641145

Solving
0.2 + x = 2.457641145

Solving for variable 'x'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + x = 2.457641145 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + x = 2.457641145 + -0.2
x = 2.457641145 + -0.2

Combine like terms: 2.457641145 + -0.2 = 2.257641145
x = 2.257641145

Simplifying
x = 2.257641145


Subproblem 2
x + 0.2 = -2.457641145

Simplifying
x + 0.2 = -2.457641145

Reorder the terms:
0.2 + x = -2.457641145

Solving
0.2 + x = -2.457641145

Solving for variable 'x'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + x = -2.457641145 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + x = -2.457641145 + -0.2
x = -2.457641145 + -0.2

Combine like terms: -2.457641145 + -0.2 = -2.657641145
x = -2.657641145

Simplifying
x = -2.657641145


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.257641145, -2.657641145}
Solution
x = {2.257641145, -2.657641145}

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