2(x-10)-10(x+9)=5x(2x-4)-2

Solution for 2(x-10)-10(x+9)=5x(2x-4)-2 equation:

Simplifying
2(x + -10) + -10(x + 9) = 5x(2x + -4) + -2

Reorder the terms:
2(-10 + x) + -10(x + 9) = 5x(2x + -4) + -2
(-10 * 2 + x * 2) + -10(x + 9) = 5x(2x + -4) + -2
(-20 + 2x) + -10(x + 9) = 5x(2x + -4) + -2

Reorder the terms:
-20 + 2x + -10(9 + x) = 5x(2x + -4) + -2
-20 + 2x + (9 * -10 + x * -10) = 5x(2x + -4) + -2
-20 + 2x + (-90 + -10x) = 5x(2x + -4) + -2

Reorder the terms:
-20 + -90 + 2x + -10x = 5x(2x + -4) + -2

Combine like terms: -20 + -90 = -110
-110 + 2x + -10x = 5x(2x + -4) + -2

Combine like terms: 2x + -10x = -8x
-110 + -8x = 5x(2x + -4) + -2

Reorder the terms:
-110 + -8x = 5x(-4 + 2x) + -2
-110 + -8x = (-4 * 5x + 2x * 5x) + -2
-110 + -8x = (-20x + 10x2) + -2

Reorder the terms:
-110 + -8x = -2 + -20x + 10x2

Solving
-110 + -8x = -2 + -20x + 10x2

Solving for variable 'x'.

Reorder the terms:
-110 + 2 + -8x + 20x + -10x2 = -2 + -20x + 10x2 + 2 + 20x + -10x2

Combine like terms: -110 + 2 = -108
-108 + -8x + 20x + -10x2 = -2 + -20x + 10x2 + 2 + 20x + -10x2

Combine like terms: -8x + 20x = 12x
-108 + 12x + -10x2 = -2 + -20x + 10x2 + 2 + 20x + -10x2

Reorder the terms:
-108 + 12x + -10x2 = -2 + 2 + -20x + 20x + 10x2 + -10x2

Combine like terms: -2 + 2 = 0
-108 + 12x + -10x2 = 0 + -20x + 20x + 10x2 + -10x2
-108 + 12x + -10x2 = -20x + 20x + 10x2 + -10x2

Combine like terms: -20x + 20x = 0
-108 + 12x + -10x2 = 0 + 10x2 + -10x2
-108 + 12x + -10x2 = 10x2 + -10x2

Combine like terms: 10x2 + -10x2 = 0
-108 + 12x + -10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-54 + 6x + -5x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-54 + 6x + -5x2)' equal to zero and attempt to solve:

Simplifying
-54 + 6x + -5x2 = 0

Solving
-54 + 6x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
10.8 + -1.2x + x2 = 0

Move the constant term to the right:

Add '-10.8' to each side of the equation.
10.8 + -1.2x + -10.8 + x2 = 0 + -10.8

Reorder the terms:
10.8 + -10.8 + -1.2x + x2 = 0 + -10.8

Combine like terms: 10.8 + -10.8 = 0.0
0.0 + -1.2x + x2 = 0 + -10.8
-1.2x + x2 = 0 + -10.8

Combine like terms: 0 + -10.8 = -10.8
-1.2x + x2 = -10.8

The x term is -1.2x.  Take half its coefficient (-0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
-1.2x + 0.36 + x2 = -10.8 + 0.36

Reorder the terms:
0.36 + -1.2x + x2 = -10.8 + 0.36

Combine like terms: -10.8 + 0.36 = -10.44
0.36 + -1.2x + x2 = -10.44

Factor a perfect square on the left side:
(x + -0.6)(x + -0.6) = -10.44

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.