(x-2)(x+2)=4x^2+x-10

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

Simplifying
(x + -2)(x + 2) = 4x2 + x + -10

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

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

Multiply (-2 + x) * (2 + x)
(-2(2 + x) + x(2 + x)) = 4x2 + x + -10
((2 * -2 + x * -2) + x(2 + x)) = 4x2 + x + -10
((-4 + -2x) + x(2 + x)) = 4x2 + x + -10
(-4 + -2x + (2 * x + x * x)) = 4x2 + x + -10
(-4 + -2x + (2x + x2)) = 4x2 + x + -10

Combine like terms: -2x + 2x = 0
(-4 + 0 + x2) = 4x2 + x + -10
(-4 + x2) = 4x2 + x + -10

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

Solving
-4 + x2 = -10 + x + 4x2

Solving for variable 'x'.

Reorder the terms:
-4 + 10 + -1x + x2 + -4x2 = -10 + x + 4x2 + 10 + -1x + -4x2

Combine like terms: -4 + 10 = 6
6 + -1x + x2 + -4x2 = -10 + x + 4x2 + 10 + -1x + -4x2

Combine like terms: x2 + -4x2 = -3x2
6 + -1x + -3x2 = -10 + x + 4x2 + 10 + -1x + -4x2

Reorder the terms:
6 + -1x + -3x2 = -10 + 10 + x + -1x + 4x2 + -4x2

Combine like terms: -10 + 10 = 0
6 + -1x + -3x2 = 0 + x + -1x + 4x2 + -4x2
6 + -1x + -3x2 = x + -1x + 4x2 + -4x2

Combine like terms: x + -1x = 0
6 + -1x + -3x2 = 0 + 4x2 + -4x2
6 + -1x + -3x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
6 + -1x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-2 + 0.3333333333x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 0.3333333333x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 0.3333333333x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 0.3333333333x + x2 = 0 + 2
0.3333333333x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
0.3333333333x + x2 = 2

The x term is 0.3333333333x.  Take half its coefficient (0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
0.3333333333x + 0.02777777779 + x2 = 2 + 0.02777777779

Reorder the terms:
0.02777777779 + 0.3333333333x + x2 = 2 + 0.02777777779

Combine like terms: 2 + 0.02777777779 = 2.02777777779
0.02777777779 + 0.3333333333x + x2 = 2.02777777779

Factor a perfect square on the left side:
(x + 0.1666666667)(x + 0.1666666667) = 2.02777777779

Calculate the square root of the right side: 1.424000624

Break this problem into two subproblems by setting 
(x + 0.1666666667) equal to 1.424000624 and -1.424000624.

Subproblem 1
x + 0.1666666667 = 1.424000624

Simplifying
x + 0.1666666667 = 1.424000624

Reorder the terms:
0.1666666667 + x = 1.424000624

Solving
0.1666666667 + x = 1.424000624

Solving for variable 'x'.

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

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -0.1666666667 + x = 1.424000624 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + x = 1.424000624 + -0.1666666667
x = 1.424000624 + -0.1666666667

Combine like terms: 1.424000624 + -0.1666666667 = 1.2573339573
x = 1.2573339573

Simplifying
x = 1.2573339573

Subproblem 2
x + 0.1666666667 = -1.424000624

Simplifying
x + 0.1666666667 = -1.424000624

Reorder the terms:
0.1666666667 + x = -1.424000624

Solving
0.1666666667 + x = -1.424000624

Solving for variable 'x'.

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

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -0.1666666667 + x = -1.424000624 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + x = -1.424000624 + -0.1666666667
x = -1.424000624 + -0.1666666667

Combine like terms: -1.424000624 + -0.1666666667 = -1.5906672907
x = -1.5906672907

Simplifying
x = -1.5906672907

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.2573339573, -1.5906672907}