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

Solution for 5(x+2)-2(x-2)=7(x^2-4) equation:

Simplifying
5(x + 2) + -2(x + -2) = 7(x2 + -4)

Reorder the terms:
5(2 + x) + -2(x + -2) = 7(x2 + -4)
(2 * 5 + x * 5) + -2(x + -2) = 7(x2 + -4)
(10 + 5x) + -2(x + -2) = 7(x2 + -4)

Reorder the terms:
10 + 5x + -2(-2 + x) = 7(x2 + -4)
10 + 5x + (-2 * -2 + x * -2) = 7(x2 + -4)
10 + 5x + (4 + -2x) = 7(x2 + -4)

Reorder the terms:
10 + 4 + 5x + -2x = 7(x2 + -4)

Combine like terms: 10 + 4 = 14
14 + 5x + -2x = 7(x2 + -4)

Combine like terms: 5x + -2x = 3x
14 + 3x = 7(x2 + -4)

Reorder the terms:
14 + 3x = 7(-4 + x2)
14 + 3x = (-4 * 7 + x2 * 7)
14 + 3x = (-28 + 7x2)

Solving
14 + 3x = -28 + 7x2

Solving for variable 'x'.

Reorder the terms:
14 + 28 + 3x + -7x2 = -28 + 7x2 + 28 + -7x2

Combine like terms: 14 + 28 = 42
42 + 3x + -7x2 = -28 + 7x2 + 28 + -7x2

Reorder the terms:
42 + 3x + -7x2 = -28 + 28 + 7x2 + -7x2

Combine like terms: -28 + 28 = 0
42 + 3x + -7x2 = 0 + 7x2 + -7x2
42 + 3x + -7x2 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
42 + 3x + -7x2 = 0

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

Divide each side by '-7'.
-6 + -0.4285714286x + x2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -0.4285714286x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + -0.4285714286x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -0.4285714286x + x2 = 0 + 6
-0.4285714286x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
-0.4285714286x + x2 = 6

The x term is -0.4285714286x.  Take half its coefficient (-0.2142857143).
Square it (0.04591836735) and add it to both sides.

Add '0.04591836735' to each side of the equation.
-0.4285714286x + 0.04591836735 + x2 = 6 + 0.04591836735

Reorder the terms:
0.04591836735 + -0.4285714286x + x2 = 6 + 0.04591836735

Combine like terms: 6 + 0.04591836735 = 6.04591836735
0.04591836735 + -0.4285714286x + x2 = 6.04591836735

Factor a perfect square on the left side:
(x + -0.2142857143)(x + -0.2142857143) = 6.04591836735

Calculate the square root of the right side: 2.458844925

Break this problem into two subproblems by setting 
(x + -0.2142857143) equal to 2.458844925 and -2.458844925.

Subproblem 1
x + -0.2142857143 = 2.458844925

Simplifying
x + -0.2142857143 = 2.458844925

Reorder the terms:
-0.2142857143 + x = 2.458844925

Solving
-0.2142857143 + x = 2.458844925

Solving for variable 'x'.

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

Add '0.2142857143' to each side of the equation.
-0.2142857143 + 0.2142857143 + x = 2.458844925 + 0.2142857143

Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000
0.0000000000 + x = 2.458844925 + 0.2142857143
x = 2.458844925 + 0.2142857143

Combine like terms: 2.458844925 + 0.2142857143 = 2.6731306393
x = 2.6731306393

Simplifying
x = 2.6731306393

Subproblem 2
x + -0.2142857143 = -2.458844925

Simplifying
x + -0.2142857143 = -2.458844925

Reorder the terms:
-0.2142857143 + x = -2.458844925

Solving
-0.2142857143 + x = -2.458844925

Solving for variable 'x'.

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

Add '0.2142857143' to each side of the equation.
-0.2142857143 + 0.2142857143 + x = -2.458844925 + 0.2142857143

Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000
0.0000000000 + x = -2.458844925 + 0.2142857143
x = -2.458844925 + 0.2142857143

Combine like terms: -2.458844925 + 0.2142857143 = -2.2445592107
x = -2.2445592107

Simplifying
x = -2.2445592107

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.6731306393, -2.2445592107}