3(x+1)=4x(x+2)

Solution for 3(x+1)=4x(x+2) equation:

Simplifying
3(x + 1) = 4x(x + 2)

Reorder the terms:
3(1 + x) = 4x(x + 2)
(1 * 3 + x * 3) = 4x(x + 2)
(3 + 3x) = 4x(x + 2)

Reorder the terms:
3 + 3x = 4x(2 + x)
3 + 3x = (2 * 4x + x * 4x)
3 + 3x = (8x + 4x2)

Solving
3 + 3x = 8x + 4x2

Solving for variable 'x'.

Combine like terms: 3x + -8x = -5x
3 + -5x + -4x2 = 8x + 4x2 + -8x + -4x2

Reorder the terms:
3 + -5x + -4x2 = 8x + -8x + 4x2 + -4x2

Combine like terms: 8x + -8x = 0
3 + -5x + -4x2 = 0 + 4x2 + -4x2
3 + -5x + -4x2 = 4x2 + -4x2

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

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

Divide each side by '-4'.
-0.75 + 1.25x + x2 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + 1.25x + 0.75 + x2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + 1.25x + x2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + 1.25x + x2 = 0 + 0.75
1.25x + x2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
1.25x + x2 = 0.75

The x term is 1.25x.  Take half its coefficient (0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
1.25x + 0.390625 + x2 = 0.75 + 0.390625

Reorder the terms:
0.390625 + 1.25x + x2 = 0.75 + 0.390625

Combine like terms: 0.75 + 0.390625 = 1.140625
0.390625 + 1.25x + x2 = 1.140625

Factor a perfect square on the left side:
(x + 0.625)(x + 0.625) = 1.140625

Calculate the square root of the right side: 1.068000468

Break this problem into two subproblems by setting 
(x + 0.625) equal to 1.068000468 and -1.068000468.

Subproblem 1
x + 0.625 = 1.068000468

Simplifying
x + 0.625 = 1.068000468

Reorder the terms:
0.625 + x = 1.068000468

Solving
0.625 + x = 1.068000468

Solving for variable 'x'.

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

Add '-0.625' to each side of the equation.
0.625 + -0.625 + x = 1.068000468 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + x = 1.068000468 + -0.625
x = 1.068000468 + -0.625

Combine like terms: 1.068000468 + -0.625 = 0.443000468
x = 0.443000468

Simplifying
x = 0.443000468

Subproblem 2
x + 0.625 = -1.068000468

Simplifying
x + 0.625 = -1.068000468

Reorder the terms:
0.625 + x = -1.068000468

Solving
0.625 + x = -1.068000468

Solving for variable 'x'.

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

Add '-0.625' to each side of the equation.
0.625 + -0.625 + x = -1.068000468 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + x = -1.068000468 + -0.625
x = -1.068000468 + -0.625

Combine like terms: -1.068000468 + -0.625 = -1.693000468
x = -1.693000468

Simplifying
x = -1.693000468

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.443000468, -1.693000468}