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

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

Simplifying
10x + (x + 3)(x + -2) = (x + 3) * 2

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

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

Multiply (3 + x) * (-2 + x)
10x + (3(-2 + x) + x(-2 + x)) = (x + 3) * 2
10x + ((-2 * 3 + x * 3) + x(-2 + x)) = (x + 3) * 2
10x + ((-6 + 3x) + x(-2 + x)) = (x + 3) * 2
10x + (-6 + 3x + (-2 * x + x * x)) = (x + 3) * 2
10x + (-6 + 3x + (-2x + x2)) = (x + 3) * 2

Combine like terms: 3x + -2x = 1x
10x + (-6 + 1x + x2) = (x + 3) * 2

Reorder the terms:
-6 + 10x + 1x + x2 = (x + 3) * 2

Combine like terms: 10x + 1x = 11x
-6 + 11x + x2 = (x + 3) * 2

Reorder the terms:
-6 + 11x + x2 = (3 + x) * 2

Reorder the terms for easier multiplication:
-6 + 11x + x2 = 2(3 + x)
-6 + 11x + x2 = (3 * 2 + x * 2)
-6 + 11x + x2 = (6 + 2x)

Solving
-6 + 11x + x2 = 6 + 2x

Solving for variable 'x'.

Reorder the terms:
-6 + -6 + 11x + -2x + x2 = 6 + 2x + -6 + -2x

Combine like terms: -6 + -6 = -12
-12 + 11x + -2x + x2 = 6 + 2x + -6 + -2x

Combine like terms: 11x + -2x = 9x
-12 + 9x + x2 = 6 + 2x + -6 + -2x

Reorder the terms:
-12 + 9x + x2 = 6 + -6 + 2x + -2x

Combine like terms: 6 + -6 = 0
-12 + 9x + x2 = 0 + 2x + -2x
-12 + 9x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-12 + 9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + 9x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + 9x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 9x + x2 = 0 + 12
9x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
9x + x2 = 12

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = 12 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 12 + 20.25

Combine like terms: 12 + 20.25 = 32.25
20.25 + 9x + x2 = 32.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 32.25

Calculate the square root of the right side: 5.678908346

Break this problem into two subproblems by setting 
(x + 4.5) equal to 5.678908346 and -5.678908346.

Subproblem 1
x + 4.5 = 5.678908346

Simplifying
x + 4.5 = 5.678908346

Reorder the terms:
4.5 + x = 5.678908346

Solving
4.5 + x = 5.678908346

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = 5.678908346 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 5.678908346 + -4.5
x = 5.678908346 + -4.5

Combine like terms: 5.678908346 + -4.5 = 1.178908346
x = 1.178908346

Simplifying
x = 1.178908346

Subproblem 2
x + 4.5 = -5.678908346

Simplifying
x + 4.5 = -5.678908346

Reorder the terms:
4.5 + x = -5.678908346

Solving
4.5 + x = -5.678908346

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = -5.678908346 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -5.678908346 + -4.5
x = -5.678908346 + -4.5

Combine like terms: -5.678908346 + -4.5 = -10.178908346
x = -10.178908346

Simplifying
x = -10.178908346

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.178908346, -10.178908346}