2x(-x-30)=180

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Solution for 2x(-x-30)=180 equation: 


Simplifying
2x(-1x + -30) = 180

Reorder the terms:
2x(-30 + -1x) = 180
(-30 * 2x + -1x * 2x) = 180
(-60x + -2x2) = 180

Solving
-60x + -2x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + -60x + -2x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + -60x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(90 + 30x + x2) = 0

Ignore the factor -2.

Subproblem 1
Set the factor '(90 + 30x + x2)' equal to zero and attempt to solve:

Simplifying
90 + 30x + x2 = 0

Solving
90 + 30x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-90' to each side of the equation.
90 + 30x + -90 + x2 = 0 + -90

Reorder the terms:
90 + -90 + 30x + x2 = 0 + -90

Combine like terms: 90 + -90 = 0
0 + 30x + x2 = 0 + -90
30x + x2 = 0 + -90

Combine like terms: 0 + -90 = -90
30x + x2 = -90

The x term is 30x.  Take half its coefficient (15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
30x + 225 + x2 = -90 + 225

Reorder the terms:
225 + 30x + x2 = -90 + 225

Combine like terms: -90 + 225 = 135
225 + 30x + x2 = 135

Factor a perfect square on the left side:
(x + 15)(x + 15) = 135

Calculate the square root of the right side: 11.618950039

Break this problem into two subproblems by setting 
(x + 15) equal to 11.618950039 and -11.618950039.


Subproblem 1
x + 15 = 11.618950039

Simplifying
x + 15 = 11.618950039

Reorder the terms:
15 + x = 11.618950039

Solving
15 + x = 11.618950039

Solving for variable 'x'.

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

Add '-15' to each side of the equation.
15 + -15 + x = 11.618950039 + -15

Combine like terms: 15 + -15 = 0
0 + x = 11.618950039 + -15
x = 11.618950039 + -15

Combine like terms: 11.618950039 + -15 = -3.381049961
x = -3.381049961

Simplifying
x = -3.381049961


Subproblem 2
x + 15 = -11.618950039

Simplifying
x + 15 = -11.618950039

Reorder the terms:
15 + x = -11.618950039

Solving
15 + x = -11.618950039

Solving for variable 'x'.

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

Add '-15' to each side of the equation.
15 + -15 + x = -11.618950039 + -15

Combine like terms: 15 + -15 = 0
0 + x = -11.618950039 + -15
x = -11.618950039 + -15

Combine like terms: -11.618950039 + -15 = -26.618950039
x = -26.618950039

Simplifying
x = -26.618950039


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.381049961, -26.618950039}
Solution
x = {-3.381049961, -26.618950039}

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