15(x^2+45x-30)=0

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Solution for 15(x^2+45x-30)=0 equation: 


Simplifying
15(x2 + 45x + -30) = 0

Reorder the terms:
15(-30 + 45x + x2) = 0
(-30 * 15 + 45x * 15 + x2 * 15) = 0
(-450 + 675x + 15x2) = 0

Solving
-450 + 675x + 15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '15'.
15(-30 + 45x + x2) = 0

Ignore the factor 15.

Subproblem 1
Set the factor '(-30 + 45x + x2)' equal to zero and attempt to solve:

Simplifying
-30 + 45x + x2 = 0

Solving
-30 + 45x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 45x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + 45x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 45x + x2 = 0 + 30
45x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
45x + x2 = 30

The x term is 45x.  Take half its coefficient (22.5).
Square it (506.25) and add it to both sides.

Add '506.25' to each side of the equation.
45x + 506.25 + x2 = 30 + 506.25

Reorder the terms:
506.25 + 45x + x2 = 30 + 506.25

Combine like terms: 30 + 506.25 = 536.25
506.25 + 45x + x2 = 536.25

Factor a perfect square on the left side:
(x + 22.5)(x + 22.5) = 536.25

Calculate the square root of the right side: 23.157072354

Break this problem into two subproblems by setting 
(x + 22.5) equal to 23.157072354 and -23.157072354.


Subproblem 1
x + 22.5 = 23.157072354

Simplifying
x + 22.5 = 23.157072354

Reorder the terms:
22.5 + x = 23.157072354

Solving
22.5 + x = 23.157072354

Solving for variable 'x'.

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

Add '-22.5' to each side of the equation.
22.5 + -22.5 + x = 23.157072354 + -22.5

Combine like terms: 22.5 + -22.5 = 0.0
0.0 + x = 23.157072354 + -22.5
x = 23.157072354 + -22.5

Combine like terms: 23.157072354 + -22.5 = 0.657072354
x = 0.657072354

Simplifying
x = 0.657072354


Subproblem 2
x + 22.5 = -23.157072354

Simplifying
x + 22.5 = -23.157072354

Reorder the terms:
22.5 + x = -23.157072354

Solving
22.5 + x = -23.157072354

Solving for variable 'x'.

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

Add '-22.5' to each side of the equation.
22.5 + -22.5 + x = -23.157072354 + -22.5

Combine like terms: 22.5 + -22.5 = 0.0
0.0 + x = -23.157072354 + -22.5
x = -23.157072354 + -22.5

Combine like terms: -23.157072354 + -22.5 = -45.657072354
x = -45.657072354

Simplifying
x = -45.657072354


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.657072354, -45.657072354}
Solution
x = {0.657072354, -45.657072354}

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