3(x^2-4)+7(x-2)x=3

Solution for 3(x^2-4)+7(x-2)x=3 equation:

Simplifying
3(x2 + -4) + 7(x + -2) * x = 3

Reorder the terms:
3(-4 + x2) + 7(x + -2) * x = 3
(-4 * 3 + x2 * 3) + 7(x + -2) * x = 3
(-12 + 3x2) + 7(x + -2) * x = 3

Reorder the terms:
-12 + 3x2 + 7(-2 + x) * x = 3

Reorder the terms for easier multiplication:
-12 + 3x2 + 7x(-2 + x) = 3
-12 + 3x2 + (-2 * 7x + x * 7x) = 3
-12 + 3x2 + (-14x + 7x2) = 3

Reorder the terms:
-12 + -14x + 3x2 + 7x2 = 3

Combine like terms: 3x2 + 7x2 = 10x2
-12 + -14x + 10x2 = 3

Solving
-12 + -14x + 10x2 = 3

Solving for variable 'x'.

Reorder the terms:
-12 + -3 + -14x + 10x2 = 3 + -3

Combine like terms: -12 + -3 = -15
-15 + -14x + 10x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-15 + -14x + 10x2 = 0

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

Divide each side by '10'.
-1.5 + -1.4x + x2 = 0.0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + -1.4x + 1.5 + x2 = 0.0 + 1.5

Reorder the terms:
-1.5 + 1.5 + -1.4x + x2 = 0.0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + -1.4x + x2 = 0.0 + 1.5
-1.4x + x2 = 0.0 + 1.5

Combine like terms: 0.0 + 1.5 = 1.5
-1.4x + x2 = 1.5

The x term is -1.4x.  Take half its coefficient (-0.7).
Square it (0.49) and add it to both sides.

Add '0.49' to each side of the equation.
-1.4x + 0.49 + x2 = 1.5 + 0.49

Reorder the terms:
0.49 + -1.4x + x2 = 1.5 + 0.49

Combine like terms: 1.5 + 0.49 = 1.99
0.49 + -1.4x + x2 = 1.99

Factor a perfect square on the left side:
(x + -0.7)(x + -0.7) = 1.99

Calculate the square root of the right side: 1.410673598

Break this problem into two subproblems by setting 
(x + -0.7) equal to 1.410673598 and -1.410673598.

Subproblem 1
x + -0.7 = 1.410673598

Simplifying
x + -0.7 = 1.410673598

Reorder the terms:
-0.7 + x = 1.410673598

Solving
-0.7 + x = 1.410673598

Solving for variable 'x'.

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

Add '0.7' to each side of the equation.
-0.7 + 0.7 + x = 1.410673598 + 0.7

Combine like terms: -0.7 + 0.7 = 0.0
0.0 + x = 1.410673598 + 0.7
x = 1.410673598 + 0.7

Combine like terms: 1.410673598 + 0.7 = 2.110673598
x = 2.110673598

Simplifying
x = 2.110673598

Subproblem 2
x + -0.7 = -1.410673598

Simplifying
x + -0.7 = -1.410673598

Reorder the terms:
-0.7 + x = -1.410673598

Solving
-0.7 + x = -1.410673598

Solving for variable 'x'.

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

Add '0.7' to each side of the equation.
-0.7 + 0.7 + x = -1.410673598 + 0.7

Combine like terms: -0.7 + 0.7 = 0.0
0.0 + x = -1.410673598 + 0.7
x = -1.410673598 + 0.7

Combine like terms: -1.410673598 + 0.7 = -0.710673598
x = -0.710673598

Simplifying
x = -0.710673598

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.110673598, -0.710673598}