4x(2x+30)=360

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Solution for 4x(2x+30)=360 equation: 


Simplifying
4x(2x + 30) = 360

Reorder the terms:
4x(30 + 2x) = 360
(30 * 4x + 2x * 4x) = 360
(120x + 8x2) = 360

Solving
120x + 8x2 = 360

Solving for variable 'x'.

Reorder the terms:
-360 + 120x + 8x2 = 360 + -360

Combine like terms: 360 + -360 = 0
-360 + 120x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-45 + 15x + x2) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(-45 + 15x + x2)' equal to zero and attempt to solve:

Simplifying
-45 + 15x + x2 = 0

Solving
-45 + 15x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '45' to each side of the equation.
-45 + 15x + 45 + x2 = 0 + 45

Reorder the terms:
-45 + 45 + 15x + x2 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + 15x + x2 = 0 + 45
15x + x2 = 0 + 45

Combine like terms: 0 + 45 = 45
15x + x2 = 45

The x term is 15x.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15x + 56.25 + x2 = 45 + 56.25

Reorder the terms:
56.25 + 15x + x2 = 45 + 56.25

Combine like terms: 45 + 56.25 = 101.25
56.25 + 15x + x2 = 101.25

Factor a perfect square on the left side:
(x + 7.5)(x + 7.5) = 101.25

Calculate the square root of the right side: 10.062305899

Break this problem into two subproblems by setting 
(x + 7.5) equal to 10.062305899 and -10.062305899.


Subproblem 1
x + 7.5 = 10.062305899

Simplifying
x + 7.5 = 10.062305899

Reorder the terms:
7.5 + x = 10.062305899

Solving
7.5 + x = 10.062305899

Solving for variable 'x'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + x = 10.062305899 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = 10.062305899 + -7.5
x = 10.062305899 + -7.5

Combine like terms: 10.062305899 + -7.5 = 2.562305899
x = 2.562305899

Simplifying
x = 2.562305899


Subproblem 2
x + 7.5 = -10.062305899

Simplifying
x + 7.5 = -10.062305899

Reorder the terms:
7.5 + x = -10.062305899

Solving
7.5 + x = -10.062305899

Solving for variable 'x'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + x = -10.062305899 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = -10.062305899 + -7.5
x = -10.062305899 + -7.5

Combine like terms: -10.062305899 + -7.5 = -17.562305899
x = -17.562305899

Simplifying
x = -17.562305899


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.562305899, -17.562305899}
Solution
x = {2.562305899, -17.562305899}

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