5x+7(x+1)=2x(x+3)

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Solution for 5x+7(x+1)=2x(x+3) equation: 


Simplifying
5x + 7(x + 1) = 2x(x + 3)

Reorder the terms:
5x + 7(1 + x) = 2x(x + 3)
5x + (1 * 7 + x * 7) = 2x(x + 3)
5x + (7 + 7x) = 2x(x + 3)

Reorder the terms:
7 + 5x + 7x = 2x(x + 3)

Combine like terms: 5x + 7x = 12x
7 + 12x = 2x(x + 3)

Reorder the terms:
7 + 12x = 2x(3 + x)
7 + 12x = (3 * 2x + x * 2x)
7 + 12x = (6x + 2x2)

Solving
7 + 12x = 6x + 2x2

Solving for variable 'x'.

Combine like terms: 12x + -6x = 6x
7 + 6x + -2x2 = 6x + 2x2 + -6x + -2x2

Reorder the terms:
7 + 6x + -2x2 = 6x + -6x + 2x2 + -2x2

Combine like terms: 6x + -6x = 0
7 + 6x + -2x2 = 0 + 2x2 + -2x2
7 + 6x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
7 + 6x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-3.5 + -3x + x2 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + -3x + 3.5 + x2 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + -3x + x2 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + -3x + x2 = 0 + 3.5
-3x + x2 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
-3x + x2 = 3.5

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 3.5 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 3.5 + 2.25

Combine like terms: 3.5 + 2.25 = 5.75
2.25 + -3x + x2 = 5.75

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 5.75

Calculate the square root of the right side: 2.397915762

Break this problem into two subproblems by setting 
(x + -1.5) equal to 2.397915762 and -2.397915762.


Subproblem 1
x + -1.5 = 2.397915762

Simplifying
x + -1.5 = 2.397915762

Reorder the terms:
-1.5 + x = 2.397915762

Solving
-1.5 + x = 2.397915762

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 2.397915762 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 2.397915762 + 1.5
x = 2.397915762 + 1.5

Combine like terms: 2.397915762 + 1.5 = 3.897915762
x = 3.897915762

Simplifying
x = 3.897915762


Subproblem 2
x + -1.5 = -2.397915762

Simplifying
x + -1.5 = -2.397915762

Reorder the terms:
-1.5 + x = -2.397915762

Solving
-1.5 + x = -2.397915762

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -2.397915762 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -2.397915762 + 1.5
x = -2.397915762 + 1.5

Combine like terms: -2.397915762 + 1.5 = -0.897915762
x = -0.897915762

Simplifying
x = -0.897915762


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.897915762, -0.897915762}

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