(x+10)(2x-30)=360

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Solution for (x+10)(2x-30)=360 equation: 


Simplifying
(x + 10)(2x + -30) = 360

Reorder the terms:
(10 + x)(2x + -30) = 360

Reorder the terms:
(10 + x)(-30 + 2x) = 360

Multiply (10 + x) * (-30 + 2x)
(10(-30 + 2x) + x(-30 + 2x)) = 360
((-30 * 10 + 2x * 10) + x(-30 + 2x)) = 360
((-300 + 20x) + x(-30 + 2x)) = 360
(-300 + 20x + (-30 * x + 2x * x)) = 360
(-300 + 20x + (-30x + 2x2)) = 360

Combine like terms: 20x + -30x = -10x
(-300 + -10x + 2x2) = 360

Solving
-300 + -10x + 2x2 = 360

Solving for variable 'x'.

Reorder the terms:
-300 + -360 + -10x + 2x2 = 360 + -360

Combine like terms: -300 + -360 = -660
-660 + -10x + 2x2 = 360 + -360

Combine like terms: 360 + -360 = 0
-660 + -10x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-330 + -5x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-330 + -5x + x2)' equal to zero and attempt to solve:

Simplifying
-330 + -5x + x2 = 0

Solving
-330 + -5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '330' to each side of the equation.
-330 + -5x + 330 + x2 = 0 + 330

Reorder the terms:
-330 + 330 + -5x + x2 = 0 + 330

Combine like terms: -330 + 330 = 0
0 + -5x + x2 = 0 + 330
-5x + x2 = 0 + 330

Combine like terms: 0 + 330 = 330
-5x + x2 = 330

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 = 330 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 330 + 6.25

Combine like terms: 330 + 6.25 = 336.25
6.25 + -5x + x2 = 336.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 336.25

Calculate the square root of the right side: 18.337120821

Break this problem into two subproblems by setting 
(x + -2.5) equal to 18.337120821 and -18.337120821.


Subproblem 1
x + -2.5 = 18.337120821

Simplifying
x + -2.5 = 18.337120821

Reorder the terms:
-2.5 + x = 18.337120821

Solving
-2.5 + x = 18.337120821

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 = 18.337120821 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 18.337120821 + 2.5
x = 18.337120821 + 2.5

Combine like terms: 18.337120821 + 2.5 = 20.837120821
x = 20.837120821

Simplifying
x = 20.837120821


Subproblem 2
x + -2.5 = -18.337120821

Simplifying
x + -2.5 = -18.337120821

Reorder the terms:
-2.5 + x = -18.337120821

Solving
-2.5 + x = -18.337120821

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 = -18.337120821 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -18.337120821 + 2.5
x = -18.337120821 + 2.5

Combine like terms: -18.337120821 + 2.5 = -15.837120821
x = -15.837120821

Simplifying
x = -15.837120821


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {20.837120821, -15.837120821}
Solution
x = {20.837120821, -15.837120821}

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