5x(x+3)-7(x+5)=5

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Solution for 5x(x+3)-7(x+5)=5 equation: 


Simplifying
5x(x + 3) + -7(x + 5) = 5

Reorder the terms:
5x(3 + x) + -7(x + 5) = 5
(3 * 5x + x * 5x) + -7(x + 5) = 5
(15x + 5x2) + -7(x + 5) = 5

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

Reorder the terms:
-35 + 15x + -7x + 5x2 = 5

Combine like terms: 15x + -7x = 8x
-35 + 8x + 5x2 = 5

Solving
-35 + 8x + 5x2 = 5

Solving for variable 'x'.

Reorder the terms:
-35 + -5 + 8x + 5x2 = 5 + -5

Combine like terms: -35 + -5 = -40
-40 + 8x + 5x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-40 + 8x + 5x2 = 0

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

Divide each side by '5'.
-8 + 1.6x + x2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 1.6x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + 1.6x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 1.6x + x2 = 0 + 8
1.6x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
1.6x + x2 = 8

The x term is 1.6x.  Take half its coefficient (0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
1.6x + 0.64 + x2 = 8 + 0.64

Reorder the terms:
0.64 + 1.6x + x2 = 8 + 0.64

Combine like terms: 8 + 0.64 = 8.64
0.64 + 1.6x + x2 = 8.64

Factor a perfect square on the left side:
(x + 0.8)(x + 0.8) = 8.64

Calculate the square root of the right side: 2.939387691

Break this problem into two subproblems by setting 
(x + 0.8) equal to 2.939387691 and -2.939387691.


Subproblem 1
x + 0.8 = 2.939387691

Simplifying
x + 0.8 = 2.939387691

Reorder the terms:
0.8 + x = 2.939387691

Solving
0.8 + x = 2.939387691

Solving for variable 'x'.

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

Add '-0.8' to each side of the equation.
0.8 + -0.8 + x = 2.939387691 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + x = 2.939387691 + -0.8
x = 2.939387691 + -0.8

Combine like terms: 2.939387691 + -0.8 = 2.139387691
x = 2.139387691

Simplifying
x = 2.139387691


Subproblem 2
x + 0.8 = -2.939387691

Simplifying
x + 0.8 = -2.939387691

Reorder the terms:
0.8 + x = -2.939387691

Solving
0.8 + x = -2.939387691

Solving for variable 'x'.

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

Add '-0.8' to each side of the equation.
0.8 + -0.8 + x = -2.939387691 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + x = -2.939387691 + -0.8
x = -2.939387691 + -0.8

Combine like terms: -2.939387691 + -0.8 = -3.739387691
x = -3.739387691

Simplifying
x = -3.739387691


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.139387691, -3.739387691}

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