5x^2-1(-2x+3)(3+2x)=(3+2x)2

Solution for 5x^2-1(-2x+3)(3+2x)=(3+2x)2 equation:

Simplifying
5x2 + -1(-2x + 3)(3 + 2x) = (3 + 2x) * 2

Reorder the terms:
5x2 + -1(3 + -2x)(3 + 2x) = (3 + 2x) * 2

Multiply (3 + -2x) * (3 + 2x)
5x2 + -1(3(3 + 2x) + -2x * (3 + 2x)) = (3 + 2x) * 2
5x2 + -1((3 * 3 + 2x * 3) + -2x * (3 + 2x)) = (3 + 2x) * 2
5x2 + -1((9 + 6x) + -2x * (3 + 2x)) = (3 + 2x) * 2
5x2 + -1(9 + 6x + (3 * -2x + 2x * -2x)) = (3 + 2x) * 2
5x2 + -1(9 + 6x + (-6x + -4x2)) = (3 + 2x) * 2

Combine like terms: 6x + -6x = 0
5x2 + -1(9 + 0 + -4x2) = (3 + 2x) * 2
5x2 + -1(9 + -4x2) = (3 + 2x) * 2
5x2 + (9 * -1 + -4x2 * -1) = (3 + 2x) * 2
5x2 + (-9 + 4x2) = (3 + 2x) * 2

Reorder the terms:
-9 + 5x2 + 4x2 = (3 + 2x) * 2

Combine like terms: 5x2 + 4x2 = 9x2
-9 + 9x2 = (3 + 2x) * 2

Reorder the terms for easier multiplication:
-9 + 9x2 = 2(3 + 2x)
-9 + 9x2 = (3 * 2 + 2x * 2)
-9 + 9x2 = (6 + 4x)

Solving
-9 + 9x2 = 6 + 4x

Solving for variable 'x'.

Reorder the terms:
-9 + -6 + -4x + 9x2 = 6 + 4x + -6 + -4x

Combine like terms: -9 + -6 = -15
-15 + -4x + 9x2 = 6 + 4x + -6 + -4x

Reorder the terms:
-15 + -4x + 9x2 = 6 + -6 + 4x + -4x

Combine like terms: 6 + -6 = 0
-15 + -4x + 9x2 = 0 + 4x + -4x
-15 + -4x + 9x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-15 + -4x + 9x2 = 0

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

Divide each side by '9'.
-1.666666667 + -0.4444444444x + x2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + -0.4444444444x + 1.666666667 + x2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + -0.4444444444x + x2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + -0.4444444444x + x2 = 0 + 1.666666667
-0.4444444444x + x2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
-0.4444444444x + x2 = 1.666666667

The x term is -0.4444444444x.  Take half its coefficient (-0.2222222222).
Square it (0.04938271604) and add it to both sides.

Add '0.04938271604' to each side of the equation.
-0.4444444444x + 0.04938271604 + x2 = 1.666666667 + 0.04938271604

Reorder the terms:
0.04938271604 + -0.4444444444x + x2 = 1.666666667 + 0.04938271604

Combine like terms: 1.666666667 + 0.04938271604 = 1.71604938304
0.04938271604 + -0.4444444444x + x2 = 1.71604938304

Factor a perfect square on the left side:
(x + -0.2222222222)(x + -0.2222222222) = 1.71604938304

Calculate the square root of the right side: 1.30998068

Break this problem into two subproblems by setting 
(x + -0.2222222222) equal to 1.30998068 and -1.30998068.

Subproblem 1
x + -0.2222222222 = 1.30998068

Simplifying
x + -0.2222222222 = 1.30998068

Reorder the terms:
-0.2222222222 + x = 1.30998068

Solving
-0.2222222222 + x = 1.30998068

Solving for variable 'x'.

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

Add '0.2222222222' to each side of the equation.
-0.2222222222 + 0.2222222222 + x = 1.30998068 + 0.2222222222

Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000
0.0000000000 + x = 1.30998068 + 0.2222222222
x = 1.30998068 + 0.2222222222

Combine like terms: 1.30998068 + 0.2222222222 = 1.5322029022
x = 1.5322029022

Simplifying
x = 1.5322029022

Subproblem 2
x + -0.2222222222 = -1.30998068

Simplifying
x + -0.2222222222 = -1.30998068

Reorder the terms:
-0.2222222222 + x = -1.30998068

Solving
-0.2222222222 + x = -1.30998068

Solving for variable 'x'.

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

Add '0.2222222222' to each side of the equation.
-0.2222222222 + 0.2222222222 + x = -1.30998068 + 0.2222222222

Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000
0.0000000000 + x = -1.30998068 + 0.2222222222
x = -1.30998068 + 0.2222222222

Combine like terms: -1.30998068 + 0.2222222222 = -1.0877584578
x = -1.0877584578

Simplifying
x = -1.0877584578

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.5322029022, -1.0877584578}