10x(x+2)-32=4x+3(x-2)

Solution for 10x(x+2)-32=4x+3(x-2) equation:

Simplifying
10x(x + 2) + -32 = 4x + 3(x + -2)

Reorder the terms:
10x(2 + x) + -32 = 4x + 3(x + -2)
(2 * 10x + x * 10x) + -32 = 4x + 3(x + -2)
(20x + 10x2) + -32 = 4x + 3(x + -2)

Reorder the terms:
-32 + 20x + 10x2 = 4x + 3(x + -2)

Reorder the terms:
-32 + 20x + 10x2 = 4x + 3(-2 + x)
-32 + 20x + 10x2 = 4x + (-2 * 3 + x * 3)
-32 + 20x + 10x2 = 4x + (-6 + 3x)

Reorder the terms:
-32 + 20x + 10x2 = -6 + 4x + 3x

Combine like terms: 4x + 3x = 7x
-32 + 20x + 10x2 = -6 + 7x

Solving
-32 + 20x + 10x2 = -6 + 7x

Solving for variable 'x'.

Reorder the terms:
-32 + 6 + 20x + -7x + 10x2 = -6 + 7x + 6 + -7x

Combine like terms: -32 + 6 = -26
-26 + 20x + -7x + 10x2 = -6 + 7x + 6 + -7x

Combine like terms: 20x + -7x = 13x
-26 + 13x + 10x2 = -6 + 7x + 6 + -7x

Reorder the terms:
-26 + 13x + 10x2 = -6 + 6 + 7x + -7x

Combine like terms: -6 + 6 = 0
-26 + 13x + 10x2 = 0 + 7x + -7x
-26 + 13x + 10x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-26 + 13x + 10x2 = 0

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

Divide each side by '10'.
-2.6 + 1.3x + x2 = 0

Move the constant term to the right:

Add '2.6' to each side of the equation.
-2.6 + 1.3x + 2.6 + x2 = 0 + 2.6

Reorder the terms:
-2.6 + 2.6 + 1.3x + x2 = 0 + 2.6

Combine like terms: -2.6 + 2.6 = 0.0
0.0 + 1.3x + x2 = 0 + 2.6
1.3x + x2 = 0 + 2.6

Combine like terms: 0 + 2.6 = 2.6
1.3x + x2 = 2.6

The x term is 1.3x.  Take half its coefficient (0.65).
Square it (0.4225) and add it to both sides.

Add '0.4225' to each side of the equation.
1.3x + 0.4225 + x2 = 2.6 + 0.4225

Reorder the terms:
0.4225 + 1.3x + x2 = 2.6 + 0.4225

Combine like terms: 2.6 + 0.4225 = 3.0225
0.4225 + 1.3x + x2 = 3.0225

Factor a perfect square on the left side:
(x + 0.65)(x + 0.65) = 3.0225

Calculate the square root of the right side: 1.738533865

Break this problem into two subproblems by setting 
(x + 0.65) equal to 1.738533865 and -1.738533865.

Subproblem 1
x + 0.65 = 1.738533865

Simplifying
x + 0.65 = 1.738533865

Reorder the terms:
0.65 + x = 1.738533865

Solving
0.65 + x = 1.738533865

Solving for variable 'x'.

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

Add '-0.65' to each side of the equation.
0.65 + -0.65 + x = 1.738533865 + -0.65

Combine like terms: 0.65 + -0.65 = 0.00
0.00 + x = 1.738533865 + -0.65
x = 1.738533865 + -0.65

Combine like terms: 1.738533865 + -0.65 = 1.088533865
x = 1.088533865

Simplifying
x = 1.088533865

Subproblem 2
x + 0.65 = -1.738533865

Simplifying
x + 0.65 = -1.738533865

Reorder the terms:
0.65 + x = -1.738533865

Solving
0.65 + x = -1.738533865

Solving for variable 'x'.

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

Add '-0.65' to each side of the equation.
0.65 + -0.65 + x = -1.738533865 + -0.65

Combine like terms: 0.65 + -0.65 = 0.00
0.00 + x = -1.738533865 + -0.65
x = -1.738533865 + -0.65

Combine like terms: -1.738533865 + -0.65 = -2.388533865
x = -2.388533865

Simplifying
x = -2.388533865

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.088533865, -2.388533865}