2x(4x+6)+60=180

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Solution for 2x(4x+6)+60=180 equation: 


Simplifying
2x(4x + 6) + 60 = 180

Reorder the terms:
2x(6 + 4x) + 60 = 180
(6 * 2x + 4x * 2x) + 60 = 180
(12x + 8x2) + 60 = 180

Reorder the terms:
60 + 12x + 8x2 = 180

Solving
60 + 12x + 8x2 = 180

Solving for variable 'x'.

Reorder the terms:
60 + -180 + 12x + 8x2 = 180 + -180

Combine like terms: 60 + -180 = -120
-120 + 12x + 8x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-120 + 12x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-30 + 3x + 2x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-30 + 3x + 2x2)' equal to zero and attempt to solve:

Simplifying
-30 + 3x + 2x2 = 0

Solving
-30 + 3x + 2x2 = 0

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

Divide each side by '2'.
-15 + 1.5x + x2 = 0

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + 1.5x + 15 + x2 = 0 + 15

Reorder the terms:
-15 + 15 + 1.5x + x2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 1.5x + x2 = 0 + 15
1.5x + x2 = 0 + 15

Combine like terms: 0 + 15 = 15
1.5x + x2 = 15

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 15 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 15 + 0.5625

Combine like terms: 15 + 0.5625 = 15.5625
0.5625 + 1.5x + x2 = 15.5625

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 15.5625

Calculate the square root of the right side: 3.94493346

Break this problem into two subproblems by setting 
(x + 0.75) equal to 3.94493346 and -3.94493346.


Subproblem 1
x + 0.75 = 3.94493346

Simplifying
x + 0.75 = 3.94493346

Reorder the terms:
0.75 + x = 3.94493346

Solving
0.75 + x = 3.94493346

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = 3.94493346 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 3.94493346 + -0.75
x = 3.94493346 + -0.75

Combine like terms: 3.94493346 + -0.75 = 3.19493346
x = 3.19493346

Simplifying
x = 3.19493346


Subproblem 2
x + 0.75 = -3.94493346

Simplifying
x + 0.75 = -3.94493346

Reorder the terms:
0.75 + x = -3.94493346

Solving
0.75 + x = -3.94493346

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = -3.94493346 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -3.94493346 + -0.75
x = -3.94493346 + -0.75

Combine like terms: -3.94493346 + -0.75 = -4.69493346
x = -4.69493346

Simplifying
x = -4.69493346


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.19493346, -4.69493346}
Solution
x = {3.19493346, -4.69493346}

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