x(2x-4)-83=4(6-x)

Solution for x(2x-4)-83=4(6-x) equation:

Simplifying
x(2x + -4) + -83 = 4(6 + -1x)

Reorder the terms:
x(-4 + 2x) + -83 = 4(6 + -1x)
(-4 * x + 2x * x) + -83 = 4(6 + -1x)
(-4x + 2x2) + -83 = 4(6 + -1x)

Reorder the terms:
-83 + -4x + 2x2 = 4(6 + -1x)
-83 + -4x + 2x2 = (6 * 4 + -1x * 4)
-83 + -4x + 2x2 = (24 + -4x)

Add '4x' to each side of the equation.
-83 + -4x + 4x + 2x2 = 24 + -4x + 4x

Combine like terms: -4x + 4x = 0
-83 + 0 + 2x2 = 24 + -4x + 4x
-83 + 2x2 = 24 + -4x + 4x

Combine like terms: -4x + 4x = 0
-83 + 2x2 = 24 + 0
-83 + 2x2 = 24

Solving
-83 + 2x2 = 24

Solving for variable 'x'.

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

Add '83' to each side of the equation.
-83 + 83 + 2x2 = 24 + 83

Combine like terms: -83 + 83 = 0
0 + 2x2 = 24 + 83
2x2 = 24 + 83

Combine like terms: 24 + 83 = 107
2x2 = 107

Divide each side by '2'.
x2 = 53.5

Simplifying
x2 = 53.5

Take the square root of each side:
x = {-7.314369419, 7.314369419}