(3x-7)2-5(2x+1)(x-2)=-[-(3x+1)]

Solution for (3x-7)2-5(2x+1)(x-2)=-[-(3x+1)] equation:

Simplifying
(3x + -7) * 2 + -5(2x + 1)(x + -2) = -1[-1(3x + 1)]

Reorder the terms:
(-7 + 3x) * 2 + -5(2x + 1)(x + -2) = -1[-1(3x + 1)]

Reorder the terms for easier multiplication:
2(-7 + 3x) + -5(2x + 1)(x + -2) = -1[-1(3x + 1)]
(-7 * 2 + 3x * 2) + -5(2x + 1)(x + -2) = -1[-1(3x + 1)]
(-14 + 6x) + -5(2x + 1)(x + -2) = -1[-1(3x + 1)]

Reorder the terms:
-14 + 6x + -5(1 + 2x)(x + -2) = -1[-1(3x + 1)]

Reorder the terms:
-14 + 6x + -5(1 + 2x)(-2 + x) = -1[-1(3x + 1)]

Multiply (1 + 2x) * (-2 + x)
-14 + 6x + -5(1(-2 + x) + 2x * (-2 + x)) = -1[-1(3x + 1)]
-14 + 6x + -5((-2 * 1 + x * 1) + 2x * (-2 + x)) = -1[-1(3x + 1)]
-14 + 6x + -5((-2 + 1x) + 2x * (-2 + x)) = -1[-1(3x + 1)]
-14 + 6x + -5(-2 + 1x + (-2 * 2x + x * 2x)) = -1[-1(3x + 1)]
-14 + 6x + -5(-2 + 1x + (-4x + 2x2)) = -1[-1(3x + 1)]

Combine like terms: 1x + -4x = -3x
-14 + 6x + -5(-2 + -3x + 2x2) = -1[-1(3x + 1)]
-14 + 6x + (-2 * -5 + -3x * -5 + 2x2 * -5) = -1[-1(3x + 1)]
-14 + 6x + (10 + 15x + -10x2) = -1[-1(3x + 1)]

Reorder the terms:
-14 + 10 + 6x + 15x + -10x2 = -1[-1(3x + 1)]

Combine like terms: -14 + 10 = -4
-4 + 6x + 15x + -10x2 = -1[-1(3x + 1)]

Combine like terms: 6x + 15x = 21x
-4 + 21x + -10x2 = -1[-1(3x + 1)]

Reorder the terms:
-4 + 21x + -10x2 = -1[-1(1 + 3x)]
-4 + 21x + -10x2 = -1[(1 * -1 + 3x * -1)]
-4 + 21x + -10x2 = -1[(-1 + -3x)]
-4 + 21x + -10x2 = [-1 * -1 + -3x * -1]
-4 + 21x + -10x2 = [1 + 3x]

Solving
-4 + 21x + -10x2 = 1 + 3x

Solving for variable 'x'.

Reorder the terms:
-4 + -1 + 21x + -3x + -10x2 = 1 + 3x + -1 + -3x

Combine like terms: -4 + -1 = -5
-5 + 21x + -3x + -10x2 = 1 + 3x + -1 + -3x

Combine like terms: 21x + -3x = 18x
-5 + 18x + -10x2 = 1 + 3x + -1 + -3x

Reorder the terms:
-5 + 18x + -10x2 = 1 + -1 + 3x + -3x

Combine like terms: 1 + -1 = 0
-5 + 18x + -10x2 = 0 + 3x + -3x
-5 + 18x + -10x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-5 + 18x + -10x2 = 0

Begin completing the square.  Divide all terms by
-10 the coefficient of the squared term: 

Divide each side by '-10'.
0.5 + -1.8x + x2 = 0.0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -1.8x + -0.5 + x2 = 0.0 + -0.5

Reorder the terms:
0.5 + -0.5 + -1.8x + x2 = 0.0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -1.8x + x2 = 0.0 + -0.5
-1.8x + x2 = 0.0 + -0.5

Combine like terms: 0.0 + -0.5 = -0.5
-1.8x + x2 = -0.5

The x term is -1.8x.  Take half its coefficient (-0.9).
Square it (0.81) and add it to both sides.

Add '0.81' to each side of the equation.
-1.8x + 0.81 + x2 = -0.5 + 0.81

Reorder the terms:
0.81 + -1.8x + x2 = -0.5 + 0.81

Combine like terms: -0.5 + 0.81 = 0.31
0.81 + -1.8x + x2 = 0.31

Factor a perfect square on the left side:
(x + -0.9)(x + -0.9) = 0.31

Calculate the square root of the right side: 0.556776436

Break this problem into two subproblems by setting 
(x + -0.9) equal to 0.556776436 and -0.556776436.

Subproblem 1
x + -0.9 = 0.556776436

Simplifying
x + -0.9 = 0.556776436

Reorder the terms:
-0.9 + x = 0.556776436

Solving
-0.9 + x = 0.556776436

Solving for variable 'x'.

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

Add '0.9' to each side of the equation.
-0.9 + 0.9 + x = 0.556776436 + 0.9

Combine like terms: -0.9 + 0.9 = 0.0
0.0 + x = 0.556776436 + 0.9
x = 0.556776436 + 0.9

Combine like terms: 0.556776436 + 0.9 = 1.456776436
x = 1.456776436

Simplifying
x = 1.456776436

Subproblem 2
x + -0.9 = -0.556776436

Simplifying
x + -0.9 = -0.556776436

Reorder the terms:
-0.9 + x = -0.556776436

Solving
-0.9 + x = -0.556776436

Solving for variable 'x'.

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

Add '0.9' to each side of the equation.
-0.9 + 0.9 + x = -0.556776436 + 0.9

Combine like terms: -0.9 + 0.9 = 0.0
0.0 + x = -0.556776436 + 0.9
x = -0.556776436 + 0.9

Combine like terms: -0.556776436 + 0.9 = 0.343223564
x = 0.343223564

Simplifying
x = 0.343223564

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.456776436, 0.343223564}