5(3x-5)4(14-2x)-2(3x+3)=-2

Solution for 5(3x-5)4(14-2x)-2(3x+3)=-2 equation:

Simplifying
5(3x + -5) * 4(14 + -2x) + -2(3x + 3) = -2

Reorder the terms:
5(-5 + 3x) * 4(14 + -2x) + -2(3x + 3) = -2

Reorder the terms for easier multiplication:
5 * 4(-5 + 3x)(14 + -2x) + -2(3x + 3) = -2

Multiply 5 * 4
20(-5 + 3x)(14 + -2x) + -2(3x + 3) = -2

Multiply (-5 + 3x) * (14 + -2x)
20(-5(14 + -2x) + 3x * (14 + -2x)) + -2(3x + 3) = -2
20((14 * -5 + -2x * -5) + 3x * (14 + -2x)) + -2(3x + 3) = -2
20((-70 + 10x) + 3x * (14 + -2x)) + -2(3x + 3) = -2
20(-70 + 10x + (14 * 3x + -2x * 3x)) + -2(3x + 3) = -2
20(-70 + 10x + (42x + -6x2)) + -2(3x + 3) = -2

Combine like terms: 10x + 42x = 52x
20(-70 + 52x + -6x2) + -2(3x + 3) = -2
(-70 * 20 + 52x * 20 + -6x2 * 20) + -2(3x + 3) = -2
(-1400 + 1040x + -120x2) + -2(3x + 3) = -2

Reorder the terms:
-1400 + 1040x + -120x2 + -2(3 + 3x) = -2
-1400 + 1040x + -120x2 + (3 * -2 + 3x * -2) = -2
-1400 + 1040x + -120x2 + (-6 + -6x) = -2

Reorder the terms:
-1400 + -6 + 1040x + -6x + -120x2 = -2

Combine like terms: -1400 + -6 = -1406
-1406 + 1040x + -6x + -120x2 = -2

Combine like terms: 1040x + -6x = 1034x
-1406 + 1034x + -120x2 = -2

Solving
-1406 + 1034x + -120x2 = -2

Solving for variable 'x'.

Reorder the terms:
-1406 + 2 + 1034x + -120x2 = -2 + 2

Combine like terms: -1406 + 2 = -1404
-1404 + 1034x + -120x2 = -2 + 2

Combine like terms: -2 + 2 = 0
-1404 + 1034x + -120x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-702 + 517x + -60x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-702 + 517x + -60x2)' equal to zero and attempt to solve:

Simplifying
-702 + 517x + -60x2 = 0

Solving
-702 + 517x + -60x2 = 0

Begin completing the square.  Divide all terms by
-60 the coefficient of the squared term: 

Divide each side by '-60'.
11.7 + -8.616666667x + x2 = 0.0

Move the constant term to the right:

Add '-11.7' to each side of the equation.
11.7 + -8.616666667x + -11.7 + x2 = 0.0 + -11.7

Reorder the terms:
11.7 + -11.7 + -8.616666667x + x2 = 0.0 + -11.7

Combine like terms: 11.7 + -11.7 = 0.0
0.0 + -8.616666667x + x2 = 0.0 + -11.7
-8.616666667x + x2 = 0.0 + -11.7

Combine like terms: 0.0 + -11.7 = -11.7
-8.616666667x + x2 = -11.7

The x term is -8.616666667x.  Take half its coefficient (-4.308333334).
Square it (18.56173612) and add it to both sides.

Add '18.56173612' to each side of the equation.
-8.616666667x + 18.56173612 + x2 = -11.7 + 18.56173612

Reorder the terms:
18.56173612 + -8.616666667x + x2 = -11.7 + 18.56173612

Combine like terms: -11.7 + 18.56173612 = 6.86173612
18.56173612 + -8.616666667x + x2 = 6.86173612

Factor a perfect square on the left side:
(x + -4.308333334)(x + -4.308333334) = 6.86173612

Calculate the square root of the right side: 2.619491577

Break this problem into two subproblems by setting 
(x + -4.308333334) equal to 2.619491577 and -2.619491577.

Subproblem 1
x + -4.308333334 = 2.619491577

Simplifying
x + -4.308333334 = 2.619491577

Reorder the terms:
-4.308333334 + x = 2.619491577

Solving
-4.308333334 + x = 2.619491577

Solving for variable 'x'.

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

Add '4.308333334' to each side of the equation.
-4.308333334 + 4.308333334 + x = 2.619491577 + 4.308333334

Combine like terms: -4.308333334 + 4.308333334 = 0.000000000
0.000000000 + x = 2.619491577 + 4.308333334
x = 2.619491577 + 4.308333334

Combine like terms: 2.619491577 + 4.308333334 = 6.927824911
x = 6.927824911

Simplifying
x = 6.927824911

Subproblem 2
x + -4.308333334 = -2.619491577

Simplifying
x + -4.308333334 = -2.619491577

Reorder the terms:
-4.308333334 + x = -2.619491577

Solving
-4.308333334 + x = -2.619491577

Solving for variable 'x'.

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

Add '4.308333334' to each side of the equation.
-4.308333334 + 4.308333334 + x = -2.619491577 + 4.308333334

Combine like terms: -4.308333334 + 4.308333334 = 0.000000000
0.000000000 + x = -2.619491577 + 4.308333334
x = -2.619491577 + 4.308333334

Combine like terms: -2.619491577 + 4.308333334 = 1.688841757
x = 1.688841757

Simplifying
x = 1.688841757

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.927824911, 1.688841757}
Solution
x = {6.927824911, 1.688841757}