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

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

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

Reorder the terms:
7x(2 + x) + 5 = 3x(x + 1)
(2 * 7x + x * 7x) + 5 = 3x(x + 1)
(14x + 7x2) + 5 = 3x(x + 1)

Reorder the terms:
5 + 14x + 7x2 = 3x(x + 1)

Reorder the terms:
5 + 14x + 7x2 = 3x(1 + x)
5 + 14x + 7x2 = (1 * 3x + x * 3x)
5 + 14x + 7x2 = (3x + 3x2)

Solving
5 + 14x + 7x2 = 3x + 3x2

Solving for variable 'x'.

Reorder the terms:
5 + 14x + -3x + 7x2 + -3x2 = 3x + 3x2 + -3x + -3x2

Combine like terms: 14x + -3x = 11x
5 + 11x + 7x2 + -3x2 = 3x + 3x2 + -3x + -3x2

Combine like terms: 7x2 + -3x2 = 4x2
5 + 11x + 4x2 = 3x + 3x2 + -3x + -3x2

Reorder the terms:
5 + 11x + 4x2 = 3x + -3x + 3x2 + -3x2

Combine like terms: 3x + -3x = 0
5 + 11x + 4x2 = 0 + 3x2 + -3x2
5 + 11x + 4x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
5 + 11x + 4x2 = 0

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

Divide each side by '4'.
1.25 + 2.75x + x2 = 0

Move the constant term to the right:

Add '-1.25' to each side of the equation.
1.25 + 2.75x + -1.25 + x2 = 0 + -1.25

Reorder the terms:
1.25 + -1.25 + 2.75x + x2 = 0 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + 2.75x + x2 = 0 + -1.25
2.75x + x2 = 0 + -1.25

Combine like terms: 0 + -1.25 = -1.25
2.75x + x2 = -1.25

The x term is 2.75x.  Take half its coefficient (1.375).
Square it (1.890625) and add it to both sides.

Add '1.890625' to each side of the equation.
2.75x + 1.890625 + x2 = -1.25 + 1.890625

Reorder the terms:
1.890625 + 2.75x + x2 = -1.25 + 1.890625

Combine like terms: -1.25 + 1.890625 = 0.640625
1.890625 + 2.75x + x2 = 0.640625

Factor a perfect square on the left side:
(x + 1.375)(x + 1.375) = 0.640625

Calculate the square root of the right side: 0.80039053

Break this problem into two subproblems by setting 
(x + 1.375) equal to 0.80039053 and -0.80039053.

Subproblem 1
x + 1.375 = 0.80039053

Simplifying
x + 1.375 = 0.80039053

Reorder the terms:
1.375 + x = 0.80039053

Solving
1.375 + x = 0.80039053

Solving for variable 'x'.

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

Add '-1.375' to each side of the equation.
1.375 + -1.375 + x = 0.80039053 + -1.375

Combine like terms: 1.375 + -1.375 = 0.000
0.000 + x = 0.80039053 + -1.375
x = 0.80039053 + -1.375

Combine like terms: 0.80039053 + -1.375 = -0.57460947
x = -0.57460947

Simplifying
x = -0.57460947

Subproblem 2
x + 1.375 = -0.80039053

Simplifying
x + 1.375 = -0.80039053

Reorder the terms:
1.375 + x = -0.80039053

Solving
1.375 + x = -0.80039053

Solving for variable 'x'.

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

Add '-1.375' to each side of the equation.
1.375 + -1.375 + x = -0.80039053 + -1.375

Combine like terms: 1.375 + -1.375 = 0.000
0.000 + x = -0.80039053 + -1.375
x = -0.80039053 + -1.375

Combine like terms: -0.80039053 + -1.375 = -2.17539053
x = -2.17539053

Simplifying
x = -2.17539053

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.57460947, -2.17539053}