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

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

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

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

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

Multiply (3 + 2x) * (3 + 2x)
(3(3 + 2x) + 2x * (3 + 2x)) = 10
((3 * 3 + 2x * 3) + 2x * (3 + 2x)) = 10
((9 + 6x) + 2x * (3 + 2x)) = 10
(9 + 6x + (3 * 2x + 2x * 2x)) = 10
(9 + 6x + (6x + 4x2)) = 10

Combine like terms: 6x + 6x = 12x
(9 + 12x + 4x2) = 10

Solving
9 + 12x + 4x2 = 10

Solving for variable 'x'.

Reorder the terms:
9 + -10 + 12x + 4x2 = 10 + -10

Combine like terms: 9 + -10 = -1
-1 + 12x + 4x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-1 + 12x + 4x2 = 0

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

Divide each side by '4'.
-0.25 + 3x + x2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + 3x + 0.25 + x2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + 3x + x2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + 3x + x2 = 0 + 0.25
3x + x2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
3x + x2 = 0.25

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 0.25 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 0.25 + 2.25

Combine like terms: 0.25 + 2.25 = 2.5
2.25 + 3x + x2 = 2.5

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 2.5

Calculate the square root of the right side: 1.58113883

Break this problem into two subproblems by setting 
(x + 1.5) equal to 1.58113883 and -1.58113883.

Subproblem 1
x + 1.5 = 1.58113883

Simplifying
x + 1.5 = 1.58113883

Reorder the terms:
1.5 + x = 1.58113883

Solving
1.5 + x = 1.58113883

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 1.58113883 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 1.58113883 + -1.5
x = 1.58113883 + -1.5

Combine like terms: 1.58113883 + -1.5 = 0.08113883
x = 0.08113883

Simplifying
x = 0.08113883

Subproblem 2
x + 1.5 = -1.58113883

Simplifying
x + 1.5 = -1.58113883

Reorder the terms:
1.5 + x = -1.58113883

Solving
1.5 + x = -1.58113883

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -1.58113883 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -1.58113883 + -1.5
x = -1.58113883 + -1.5

Combine like terms: -1.58113883 + -1.5 = -3.08113883
x = -3.08113883

Simplifying
x = -3.08113883

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.08113883, -3.08113883}