-3x(x+5)=-15

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Solution for -3x(x+5)=-15 equation:


Simplifying
-3x(x + 5) = -15

Reorder the terms:
-3x(5 + x) = -15
(5 * -3x + x * -3x) = -15
(-15x + -3x2) = -15

Solving
-15x + -3x2 = -15

Solving for variable 'x'.

Reorder the terms:
15 + -15x + -3x2 = -15 + 15

Combine like terms: -15 + 15 = 0
15 + -15x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(5 + -5x + -1x2) = 0

Ignore the factor 3.

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

Simplifying
5 + -5x + -1x2 = 0

Solving
5 + -5x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-5 + 5x + x2 = 0

Move the constant term to the right:

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

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

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

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

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 = 5 + 6.25

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

Combine like terms: 5 + 6.25 = 11.25
6.25 + 5x + x2 = 11.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(x + 2.5) equal to 3.354101966 and -3.354101966.


Subproblem 1
x + 2.5 = 3.354101966

Simplifying
x + 2.5 = 3.354101966

Reorder the terms:
2.5 + x = 3.354101966

Solving
2.5 + x = 3.354101966

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 = 3.354101966 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 3.354101966 + -2.5
x = 3.354101966 + -2.5

Combine like terms: 3.354101966 + -2.5 = 0.854101966
x = 0.854101966

Simplifying
x = 0.854101966


Subproblem 2
x + 2.5 = -3.354101966

Simplifying
x + 2.5 = -3.354101966

Reorder the terms:
2.5 + x = -3.354101966

Solving
2.5 + x = -3.354101966

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 = -3.354101966 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -3.354101966 + -2.5
x = -3.354101966 + -2.5

Combine like terms: -3.354101966 + -2.5 = -5.854101966
x = -5.854101966

Simplifying
x = -5.854101966


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.854101966, -5.854101966}
Solution
x = {0.854101966, -5.854101966}

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