3(x+2)4x-5=7(x+1)-6

Solution for 3(x+2)4x-5=7(x+1)-6 equation:

Simplifying
3(x + 2) * 4x + -5 = 7(x + 1) + -6

Reorder the terms:
3(2 + x) * 4x + -5 = 7(x + 1) + -6

Reorder the terms for easier multiplication:
3 * 4x(2 + x) + -5 = 7(x + 1) + -6

Multiply 3 * 4
12x(2 + x) + -5 = 7(x + 1) + -6
(2 * 12x + x * 12x) + -5 = 7(x + 1) + -6
(24x + 12x2) + -5 = 7(x + 1) + -6

Reorder the terms:
-5 + 24x + 12x2 = 7(x + 1) + -6

Reorder the terms:
-5 + 24x + 12x2 = 7(1 + x) + -6
-5 + 24x + 12x2 = (1 * 7 + x * 7) + -6
-5 + 24x + 12x2 = (7 + 7x) + -6

Reorder the terms:
-5 + 24x + 12x2 = 7 + -6 + 7x

Combine like terms: 7 + -6 = 1
-5 + 24x + 12x2 = 1 + 7x

Solving
-5 + 24x + 12x2 = 1 + 7x

Solving for variable 'x'.

Reorder the terms:
-5 + -1 + 24x + -7x + 12x2 = 1 + 7x + -1 + -7x

Combine like terms: -5 + -1 = -6
-6 + 24x + -7x + 12x2 = 1 + 7x + -1 + -7x

Combine like terms: 24x + -7x = 17x
-6 + 17x + 12x2 = 1 + 7x + -1 + -7x

Reorder the terms:
-6 + 17x + 12x2 = 1 + -1 + 7x + -7x

Combine like terms: 1 + -1 = 0
-6 + 17x + 12x2 = 0 + 7x + -7x
-6 + 17x + 12x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-6 + 17x + 12x2 = 0

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

Divide each side by '12'.
-0.5 + 1.416666667x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 1.416666667x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 1.416666667x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 1.416666667x + x2 = 0 + 0.5
1.416666667x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
1.416666667x + x2 = 0.5

The x term is 1.416666667x.  Take half its coefficient (0.7083333335).
Square it (0.5017361113) and add it to both sides.

Add '0.5017361113' to each side of the equation.
1.416666667x + 0.5017361113 + x2 = 0.5 + 0.5017361113

Reorder the terms:
0.5017361113 + 1.416666667x + x2 = 0.5 + 0.5017361113

Combine like terms: 0.5 + 0.5017361113 = 1.0017361113
0.5017361113 + 1.416666667x + x2 = 1.0017361113

Factor a perfect square on the left side:
(x + 0.7083333335)(x + 0.7083333335) = 1.0017361113

Calculate the square root of the right side: 1.000867679

Break this problem into two subproblems by setting 
(x + 0.7083333335) equal to 1.000867679 and -1.000867679.

Subproblem 1
x + 0.7083333335 = 1.000867679

Simplifying
x + 0.7083333335 = 1.000867679

Reorder the terms:
0.7083333335 + x = 1.000867679

Solving
0.7083333335 + x = 1.000867679

Solving for variable 'x'.

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

Add '-0.7083333335' to each side of the equation.
0.7083333335 + -0.7083333335 + x = 1.000867679 + -0.7083333335

Combine like terms: 0.7083333335 + -0.7083333335 = 0.0000000000
0.0000000000 + x = 1.000867679 + -0.7083333335
x = 1.000867679 + -0.7083333335

Combine like terms: 1.000867679 + -0.7083333335 = 0.2925343455
x = 0.2925343455

Simplifying
x = 0.2925343455

Subproblem 2
x + 0.7083333335 = -1.000867679

Simplifying
x + 0.7083333335 = -1.000867679

Reorder the terms:
0.7083333335 + x = -1.000867679

Solving
0.7083333335 + x = -1.000867679

Solving for variable 'x'.

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

Add '-0.7083333335' to each side of the equation.
0.7083333335 + -0.7083333335 + x = -1.000867679 + -0.7083333335

Combine like terms: 0.7083333335 + -0.7083333335 = 0.0000000000
0.0000000000 + x = -1.000867679 + -0.7083333335
x = -1.000867679 + -0.7083333335

Combine like terms: -1.000867679 + -0.7083333335 = -1.7092010125
x = -1.7092010125

Simplifying
x = -1.7092010125

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.2925343455, -1.7092010125}