3x+2x(2x-3)=8-7(x-2)

Solution for 3x+2x(2x-3)=8-7(x-2) equation:

Simplifying
3x + 2x(2x + -3) = 8 + -7(x + -2)

Reorder the terms:
3x + 2x(-3 + 2x) = 8 + -7(x + -2)
3x + (-3 * 2x + 2x * 2x) = 8 + -7(x + -2)
3x + (-6x + 4x2) = 8 + -7(x + -2)

Combine like terms: 3x + -6x = -3x
-3x + 4x2 = 8 + -7(x + -2)

Reorder the terms:
-3x + 4x2 = 8 + -7(-2 + x)
-3x + 4x2 = 8 + (-2 * -7 + x * -7)
-3x + 4x2 = 8 + (14 + -7x)

Combine like terms: 8 + 14 = 22
-3x + 4x2 = 22 + -7x

Solving
-3x + 4x2 = 22 + -7x

Solving for variable 'x'.

Reorder the terms:
-22 + -3x + 7x + 4x2 = 22 + -7x + -22 + 7x

Combine like terms: -3x + 7x = 4x
-22 + 4x + 4x2 = 22 + -7x + -22 + 7x

Reorder the terms:
-22 + 4x + 4x2 = 22 + -22 + -7x + 7x

Combine like terms: 22 + -22 = 0
-22 + 4x + 4x2 = 0 + -7x + 7x
-22 + 4x + 4x2 = -7x + 7x

Combine like terms: -7x + 7x = 0
-22 + 4x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-11 + 2x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-11 + 2x + 2x2)' equal to zero and attempt to solve:

Simplifying
-11 + 2x + 2x2 = 0

Solving
-11 + 2x + 2x2 = 0

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

Divide each side by '2'.
-5.5 + x + x2 = 0

Move the constant term to the right:

Add '5.5' to each side of the equation.
-5.5 + x + 5.5 + x2 = 0 + 5.5

Reorder the terms:
-5.5 + 5.5 + x + x2 = 0 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x + x2 = 0 + 5.5
x + x2 = 0 + 5.5

Combine like terms: 0 + 5.5 = 5.5
x + x2 = 5.5

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 5.5 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 5.5 + 0.25

Combine like terms: 5.5 + 0.25 = 5.75
1.25 + x2 = 5.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 5.75

Calculate the square root of the right side: 2.397915762

Break this problem into two subproblems by setting 
(x + 0.5) equal to 2.397915762 and -2.397915762.

Subproblem 1
x + 0.5 = 2.397915762

Simplifying
x + 0.5 = 2.397915762

Reorder the terms:
0.5 + x = 2.397915762

Solving
0.5 + x = 2.397915762

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 2.397915762 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 2.397915762 + -0.5
x = 2.397915762 + -0.5

Combine like terms: 2.397915762 + -0.5 = 1.897915762
x = 1.897915762

Simplifying
x = 1.897915762

Subproblem 2
x + 0.5 = -2.397915762

Simplifying
x + 0.5 = -2.397915762

Reorder the terms:
0.5 + x = -2.397915762

Solving
0.5 + x = -2.397915762

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -2.397915762 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -2.397915762 + -0.5
x = -2.397915762 + -0.5

Combine like terms: -2.397915762 + -0.5 = -2.897915762
x = -2.897915762

Simplifying
x = -2.897915762

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.897915762, -2.897915762}
Solution
x = {1.897915762, -2.897915762}