(2x+1)(2x-1)=-(x-2)(x+3)

Solution for (2x+1)(2x-1)=-(x-2)(x+3) equation:

Simplifying
(2x + 1)(2x + -1) = -1(x + -2)(x + 3)

Reorder the terms:
(1 + 2x)(2x + -1) = -1(x + -2)(x + 3)

Reorder the terms:
(1 + 2x)(-1 + 2x) = -1(x + -2)(x + 3)

Multiply (1 + 2x) * (-1 + 2x)
(1(-1 + 2x) + 2x * (-1 + 2x)) = -1(x + -2)(x + 3)
((-1 * 1 + 2x * 1) + 2x * (-1 + 2x)) = -1(x + -2)(x + 3)
((-1 + 2x) + 2x * (-1 + 2x)) = -1(x + -2)(x + 3)
(-1 + 2x + (-1 * 2x + 2x * 2x)) = -1(x + -2)(x + 3)
(-1 + 2x + (-2x + 4x2)) = -1(x + -2)(x + 3)

Combine like terms: 2x + -2x = 0
(-1 + 0 + 4x2) = -1(x + -2)(x + 3)
(-1 + 4x2) = -1(x + -2)(x + 3)

Reorder the terms:
-1 + 4x2 = -1(-2 + x)(x + 3)

Reorder the terms:
-1 + 4x2 = -1(-2 + x)(3 + x)

Multiply (-2 + x) * (3 + x)
-1 + 4x2 = -1(-2(3 + x) + x(3 + x))
-1 + 4x2 = -1((3 * -2 + x * -2) + x(3 + x))
-1 + 4x2 = -1((-6 + -2x) + x(3 + x))
-1 + 4x2 = -1(-6 + -2x + (3 * x + x * x))
-1 + 4x2 = -1(-6 + -2x + (3x + x2))

Combine like terms: -2x + 3x = 1x
-1 + 4x2 = -1(-6 + 1x + x2)
-1 + 4x2 = (-6 * -1 + 1x * -1 + x2 * -1)
-1 + 4x2 = (6 + -1x + -1x2)

Solving
-1 + 4x2 = 6 + -1x + -1x2

Solving for variable 'x'.

Reorder the terms:
-1 + -6 + x + 4x2 + x2 = 6 + -1x + -1x2 + -6 + x + x2

Combine like terms: -1 + -6 = -7
-7 + x + 4x2 + x2 = 6 + -1x + -1x2 + -6 + x + x2

Combine like terms: 4x2 + x2 = 5x2
-7 + x + 5x2 = 6 + -1x + -1x2 + -6 + x + x2

Reorder the terms:
-7 + x + 5x2 = 6 + -6 + -1x + x + -1x2 + x2

Combine like terms: 6 + -6 = 0
-7 + x + 5x2 = 0 + -1x + x + -1x2 + x2
-7 + x + 5x2 = -1x + x + -1x2 + x2

Combine like terms: -1x + x = 0
-7 + x + 5x2 = 0 + -1x2 + x2
-7 + x + 5x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-7 + x + 5x2 = 0

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

Divide each side by '5'.
-1.4 + 0.2x + x2 = 0

Move the constant term to the right:

Add '1.4' to each side of the equation.
-1.4 + 0.2x + 1.4 + x2 = 0 + 1.4

Reorder the terms:
-1.4 + 1.4 + 0.2x + x2 = 0 + 1.4

Combine like terms: -1.4 + 1.4 = 0.0
0.0 + 0.2x + x2 = 0 + 1.4
0.2x + x2 = 0 + 1.4

Combine like terms: 0 + 1.4 = 1.4
0.2x + x2 = 1.4

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.
0.2x + 0.25 + x2 = 1.4 + 0.25

Reorder the terms:
0.25 + 0.2x + x2 = 1.4 + 0.25

Combine like terms: 1.4 + 0.25 = 1.65
0.25 + 0.2x + x2 = 1.65

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 1.65

Calculate the square root of the right side: 1.284523258

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.284523258 and -1.284523258.

Subproblem 1
x + 0.5 = 1.284523258

Simplifying
x + 0.5 = 1.284523258

Reorder the terms:
0.5 + x = 1.284523258

Solving
0.5 + x = 1.284523258

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 = 1.284523258 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 1.284523258 + -0.5
x = 1.284523258 + -0.5

Combine like terms: 1.284523258 + -0.5 = 0.784523258
x = 0.784523258

Simplifying
x = 0.784523258

Subproblem 2
x + 0.5 = -1.284523258

Simplifying
x + 0.5 = -1.284523258

Reorder the terms:
0.5 + x = -1.284523258

Solving
0.5 + x = -1.284523258

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 = -1.284523258 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -1.284523258 + -0.5
x = -1.284523258 + -0.5

Combine like terms: -1.284523258 + -0.5 = -1.784523258
x = -1.784523258

Simplifying
x = -1.784523258

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.784523258, -1.784523258}