5x(x+7)=15(x+5)

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Solution for 5x(x+7)=15(x+5) equation: 


Simplifying
5x(x + 7) = 15(x + 5)

Reorder the terms:
5x(7 + x) = 15(x + 5)
(7 * 5x + x * 5x) = 15(x + 5)
(35x + 5x2) = 15(x + 5)

Reorder the terms:
35x + 5x2 = 15(5 + x)
35x + 5x2 = (5 * 15 + x * 15)
35x + 5x2 = (75 + 15x)

Solving
35x + 5x2 = 75 + 15x

Solving for variable 'x'.

Reorder the terms:
-75 + 35x + -15x + 5x2 = 75 + 15x + -75 + -15x

Combine like terms: 35x + -15x = 20x
-75 + 20x + 5x2 = 75 + 15x + -75 + -15x

Reorder the terms:
-75 + 20x + 5x2 = 75 + -75 + 15x + -15x

Combine like terms: 75 + -75 = 0
-75 + 20x + 5x2 = 0 + 15x + -15x
-75 + 20x + 5x2 = 15x + -15x

Combine like terms: 15x + -15x = 0
-75 + 20x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-15 + 4x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-15 + 4x + x2)' equal to zero and attempt to solve:

Simplifying
-15 + 4x + x2 = 0

Solving
-15 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + 4x + 15 + x2 = 0 + 15

Reorder the terms:
-15 + 15 + 4x + x2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 4x + x2 = 0 + 15
4x + x2 = 0 + 15

Combine like terms: 0 + 15 = 15
4x + x2 = 15

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 15 + 4

Reorder the terms:
4 + 4x + x2 = 15 + 4

Combine like terms: 15 + 4 = 19
4 + 4x + x2 = 19

Factor a perfect square on the left side:
(x + 2)(x + 2) = 19

Calculate the square root of the right side: 4.358898944

Break this problem into two subproblems by setting 
(x + 2) equal to 4.358898944 and -4.358898944.


Subproblem 1
x + 2 = 4.358898944

Simplifying
x + 2 = 4.358898944

Reorder the terms:
2 + x = 4.358898944

Solving
2 + x = 4.358898944

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 4.358898944 + -2

Combine like terms: 2 + -2 = 0
0 + x = 4.358898944 + -2
x = 4.358898944 + -2

Combine like terms: 4.358898944 + -2 = 2.358898944
x = 2.358898944

Simplifying
x = 2.358898944


Subproblem 2
x + 2 = -4.358898944

Simplifying
x + 2 = -4.358898944

Reorder the terms:
2 + x = -4.358898944

Solving
2 + x = -4.358898944

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -4.358898944 + -2

Combine like terms: 2 + -2 = 0
0 + x = -4.358898944 + -2
x = -4.358898944 + -2

Combine like terms: -4.358898944 + -2 = -6.358898944
x = -6.358898944

Simplifying
x = -6.358898944


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.358898944, -6.358898944}
Solution
x = {2.358898944, -6.358898944}

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