(3x+2)5(4+2x)=10(3x+4)-8

Solution for (3x+2)5(4+2x)=10(3x+4)-8 equation:

Simplifying
(3x + 2) * 5(4 + 2x) = 10(3x + 4) + -8

Reorder the terms:
(2 + 3x) * 5(4 + 2x) = 10(3x + 4) + -8

Reorder the terms for easier multiplication:
5(2 + 3x)(4 + 2x) = 10(3x + 4) + -8

Multiply (2 + 3x) * (4 + 2x)
5(2(4 + 2x) + 3x * (4 + 2x)) = 10(3x + 4) + -8
5((4 * 2 + 2x * 2) + 3x * (4 + 2x)) = 10(3x + 4) + -8
5((8 + 4x) + 3x * (4 + 2x)) = 10(3x + 4) + -8
5(8 + 4x + (4 * 3x + 2x * 3x)) = 10(3x + 4) + -8
5(8 + 4x + (12x + 6x2)) = 10(3x + 4) + -8

Combine like terms: 4x + 12x = 16x
5(8 + 16x + 6x2) = 10(3x + 4) + -8
(8 * 5 + 16x * 5 + 6x2 * 5) = 10(3x + 4) + -8
(40 + 80x + 30x2) = 10(3x + 4) + -8

Reorder the terms:
40 + 80x + 30x2 = 10(4 + 3x) + -8
40 + 80x + 30x2 = (4 * 10 + 3x * 10) + -8
40 + 80x + 30x2 = (40 + 30x) + -8

Reorder the terms:
40 + 80x + 30x2 = 40 + -8 + 30x

Combine like terms: 40 + -8 = 32
40 + 80x + 30x2 = 32 + 30x

Solving
40 + 80x + 30x2 = 32 + 30x

Solving for variable 'x'.

Reorder the terms:
40 + -32 + 80x + -30x + 30x2 = 32 + 30x + -32 + -30x

Combine like terms: 40 + -32 = 8
8 + 80x + -30x + 30x2 = 32 + 30x + -32 + -30x

Combine like terms: 80x + -30x = 50x
8 + 50x + 30x2 = 32 + 30x + -32 + -30x

Reorder the terms:
8 + 50x + 30x2 = 32 + -32 + 30x + -30x

Combine like terms: 32 + -32 = 0
8 + 50x + 30x2 = 0 + 30x + -30x
8 + 50x + 30x2 = 30x + -30x

Combine like terms: 30x + -30x = 0
8 + 50x + 30x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + 25x + 15x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(4 + 25x + 15x2)' equal to zero and attempt to solve:

Simplifying
4 + 25x + 15x2 = 0

Solving
4 + 25x + 15x2 = 0

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

Divide each side by '15'.
0.2666666667 + 1.666666667x + x2 = 0

Move the constant term to the right:

Add '-0.2666666667' to each side of the equation.
0.2666666667 + 1.666666667x + -0.2666666667 + x2 = 0 + -0.2666666667

Reorder the terms:
0.2666666667 + -0.2666666667 + 1.666666667x + x2 = 0 + -0.2666666667

Combine like terms: 0.2666666667 + -0.2666666667 = 0.0000000000
0.0000000000 + 1.666666667x + x2 = 0 + -0.2666666667
1.666666667x + x2 = 0 + -0.2666666667

Combine like terms: 0 + -0.2666666667 = -0.2666666667
1.666666667x + x2 = -0.2666666667

The x term is 1.666666667x.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667x + 0.6944444447 + x2 = -0.2666666667 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667x + x2 = -0.2666666667 + 0.6944444447

Combine like terms: -0.2666666667 + 0.6944444447 = 0.427777778
0.6944444447 + 1.666666667x + x2 = 0.427777778

Factor a perfect square on the left side:
(x + 0.8333333335)(x + 0.8333333335) = 0.427777778

Calculate the square root of the right side: 0.654047229

Break this problem into two subproblems by setting 
(x + 0.8333333335) equal to 0.654047229 and -0.654047229.

Subproblem 1
x + 0.8333333335 = 0.654047229

Simplifying
x + 0.8333333335 = 0.654047229

Reorder the terms:
0.8333333335 + x = 0.654047229

Solving
0.8333333335 + x = 0.654047229

Solving for variable 'x'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = 0.654047229 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = 0.654047229 + -0.8333333335
x = 0.654047229 + -0.8333333335

Combine like terms: 0.654047229 + -0.8333333335 = -0.1792861045
x = -0.1792861045

Simplifying
x = -0.1792861045

Subproblem 2
x + 0.8333333335 = -0.654047229

Simplifying
x + 0.8333333335 = -0.654047229

Reorder the terms:
0.8333333335 + x = -0.654047229

Solving
0.8333333335 + x = -0.654047229

Solving for variable 'x'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = -0.654047229 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = -0.654047229 + -0.8333333335
x = -0.654047229 + -0.8333333335

Combine like terms: -0.654047229 + -0.8333333335 = -1.4873805625
x = -1.4873805625

Simplifying
x = -1.4873805625

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.1792861045, -1.4873805625}
Solution
x = {-0.1792861045, -1.4873805625}