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

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


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

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

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

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

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

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

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

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

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

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

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

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

Solving for variable 'x'.

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

Combine like terms: 21x + x = 22x
-4 + 22x + -10x2 + 3x2 = -1x + -3x2 + x + 3x2

Combine like terms: -10x2 + 3x2 = -7x2
-4 + 22x + -7x2 = -1x + -3x2 + x + 3x2

Reorder the terms:
-4 + 22x + -7x2 = -1x + x + -3x2 + 3x2

Combine like terms: -1x + x = 0
-4 + 22x + -7x2 = 0 + -3x2 + 3x2
-4 + 22x + -7x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
-4 + 22x + -7x2 = 0

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
0.5714285714 + -3.142857143x + x2 = 0

Move the constant term to the right:

Add '-0.5714285714' to each side of the equation.
0.5714285714 + -3.142857143x + -0.5714285714 + x2 = 0 + -0.5714285714

Reorder the terms:
0.5714285714 + -0.5714285714 + -3.142857143x + x2 = 0 + -0.5714285714

Combine like terms: 0.5714285714 + -0.5714285714 = 0.0000000000
0.0000000000 + -3.142857143x + x2 = 0 + -0.5714285714
-3.142857143x + x2 = 0 + -0.5714285714

Combine like terms: 0 + -0.5714285714 = -0.5714285714
-3.142857143x + x2 = -0.5714285714

The x term is -3.142857143x.  Take half its coefficient (-1.571428572).
Square it (2.469387757) and add it to both sides.

Add '2.469387757' to each side of the equation.
-3.142857143x + 2.469387757 + x2 = -0.5714285714 + 2.469387757

Reorder the terms:
2.469387757 + -3.142857143x + x2 = -0.5714285714 + 2.469387757

Combine like terms: -0.5714285714 + 2.469387757 = 1.8979591856
2.469387757 + -3.142857143x + x2 = 1.8979591856

Factor a perfect square on the left side:
(x + -1.571428572)(x + -1.571428572) = 1.8979591856

Calculate the square root of the right side: 1.377664395

Break this problem into two subproblems by setting 
(x + -1.571428572) equal to 1.377664395 and -1.377664395.


Subproblem 1
x + -1.571428572 = 1.377664395

Simplifying
x + -1.571428572 = 1.377664395

Reorder the terms:
-1.571428572 + x = 1.377664395

Solving
-1.571428572 + x = 1.377664395

Solving for variable 'x'.

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

Add '1.571428572' to each side of the equation.
-1.571428572 + 1.571428572 + x = 1.377664395 + 1.571428572

Combine like terms: -1.571428572 + 1.571428572 = 0.000000000
0.000000000 + x = 1.377664395 + 1.571428572
x = 1.377664395 + 1.571428572

Combine like terms: 1.377664395 + 1.571428572 = 2.949092967
x = 2.949092967

Simplifying
x = 2.949092967


Subproblem 2
x + -1.571428572 = -1.377664395

Simplifying
x + -1.571428572 = -1.377664395

Reorder the terms:
-1.571428572 + x = -1.377664395

Solving
-1.571428572 + x = -1.377664395

Solving for variable 'x'.

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

Add '1.571428572' to each side of the equation.
-1.571428572 + 1.571428572 + x = -1.377664395 + 1.571428572

Combine like terms: -1.571428572 + 1.571428572 = 0.000000000
0.000000000 + x = -1.377664395 + 1.571428572
x = -1.377664395 + 1.571428572

Combine like terms: -1.377664395 + 1.571428572 = 0.193764177
x = 0.193764177

Simplifying
x = 0.193764177


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.949092967, 0.193764177}

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