(x+2)(1-4x)-(2x+3)(2x+3)=

Solution for (x+2)(1-4x)-(2x+3)(2x+3)= equation:

Simplifying
(x + 2)(1 + -4x) + -1(2x + 3)(2x + 3) = 0

Reorder the terms:
(2 + x)(1 + -4x) + -1(2x + 3)(2x + 3) = 0

Multiply (2 + x) * (1 + -4x)
(2(1 + -4x) + x(1 + -4x)) + -1(2x + 3)(2x + 3) = 0
((1 * 2 + -4x * 2) + x(1 + -4x)) + -1(2x + 3)(2x + 3) = 0
((2 + -8x) + x(1 + -4x)) + -1(2x + 3)(2x + 3) = 0
(2 + -8x + (1 * x + -4x * x)) + -1(2x + 3)(2x + 3) = 0
(2 + -8x + (1x + -4x2)) + -1(2x + 3)(2x + 3) = 0

Combine like terms: -8x + 1x = -7x
(2 + -7x + -4x2) + -1(2x + 3)(2x + 3) = 0

Reorder the terms:
2 + -7x + -4x2 + -1(3 + 2x)(2x + 3) = 0

Reorder the terms:
2 + -7x + -4x2 + -1(3 + 2x)(3 + 2x) = 0

Multiply (3 + 2x) * (3 + 2x)
2 + -7x + -4x2 + -1(3(3 + 2x) + 2x * (3 + 2x)) = 0
2 + -7x + -4x2 + -1((3 * 3 + 2x * 3) + 2x * (3 + 2x)) = 0
2 + -7x + -4x2 + -1((9 + 6x) + 2x * (3 + 2x)) = 0
2 + -7x + -4x2 + -1(9 + 6x + (3 * 2x + 2x * 2x)) = 0
2 + -7x + -4x2 + -1(9 + 6x + (6x + 4x2)) = 0

Combine like terms: 6x + 6x = 12x
2 + -7x + -4x2 + -1(9 + 12x + 4x2) = 0
2 + -7x + -4x2 + (9 * -1 + 12x * -1 + 4x2 * -1) = 0
2 + -7x + -4x2 + (-9 + -12x + -4x2) = 0

Reorder the terms:
2 + -9 + -7x + -12x + -4x2 + -4x2 = 0

Combine like terms: 2 + -9 = -7
-7 + -7x + -12x + -4x2 + -4x2 = 0

Combine like terms: -7x + -12x = -19x
-7 + -19x + -4x2 + -4x2 = 0

Combine like terms: -4x2 + -4x2 = -8x2
-7 + -19x + -8x2 = 0

Solving
-7 + -19x + -8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(7 + 19x + 8x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(7 + 19x + 8x2)' equal to zero and attempt to solve:

Simplifying
7 + 19x + 8x2 = 0

Solving
7 + 19x + 8x2 = 0

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

Divide each side by '8'.
0.875 + 2.375x + x2 = 0

Move the constant term to the right:

Add '-0.875' to each side of the equation.
0.875 + 2.375x + -0.875 + x2 = 0 + -0.875

Reorder the terms:
0.875 + -0.875 + 2.375x + x2 = 0 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + 2.375x + x2 = 0 + -0.875
2.375x + x2 = 0 + -0.875

Combine like terms: 0 + -0.875 = -0.875
2.375x + x2 = -0.875

The x term is 2.375x.  Take half its coefficient (1.1875).
Square it (1.41015625) and add it to both sides.

Add '1.41015625' to each side of the equation.
2.375x + 1.41015625 + x2 = -0.875 + 1.41015625

Reorder the terms:
1.41015625 + 2.375x + x2 = -0.875 + 1.41015625

Combine like terms: -0.875 + 1.41015625 = 0.53515625
1.41015625 + 2.375x + x2 = 0.53515625

Factor a perfect square on the left side:
(x + 1.1875)(x + 1.1875) = 0.53515625

Calculate the square root of the right side: 0.731543744

Break this problem into two subproblems by setting 
(x + 1.1875) equal to 0.731543744 and -0.731543744.

Subproblem 1
x + 1.1875 = 0.731543744

Simplifying
x + 1.1875 = 0.731543744

Reorder the terms:
1.1875 + x = 0.731543744

Solving
1.1875 + x = 0.731543744

Solving for variable 'x'.

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

Add '-1.1875' to each side of the equation.
1.1875 + -1.1875 + x = 0.731543744 + -1.1875

Combine like terms: 1.1875 + -1.1875 = 0.0000
0.0000 + x = 0.731543744 + -1.1875
x = 0.731543744 + -1.1875

Combine like terms: 0.731543744 + -1.1875 = -0.455956256
x = -0.455956256

Simplifying
x = -0.455956256

Subproblem 2
x + 1.1875 = -0.731543744

Simplifying
x + 1.1875 = -0.731543744

Reorder the terms:
1.1875 + x = -0.731543744

Solving
1.1875 + x = -0.731543744

Solving for variable 'x'.

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

Add '-1.1875' to each side of the equation.
1.1875 + -1.1875 + x = -0.731543744 + -1.1875

Combine like terms: 1.1875 + -1.1875 = 0.0000
0.0000 + x = -0.731543744 + -1.1875
x = -0.731543744 + -1.1875

Combine like terms: -0.731543744 + -1.1875 = -1.919043744
x = -1.919043744

Simplifying
x = -1.919043744

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.455956256, -1.919043744}
Solution
x = {-0.455956256, -1.919043744}