x(2x-3)-3(5-x)=83

Solution for x(2x-3)-3(5-x)=83 equation:

Simplifying
x(2x + -3) + -3(5 + -1x) = 83

Reorder the terms:
x(-3 + 2x) + -3(5 + -1x) = 83
(-3 * x + 2x * x) + -3(5 + -1x) = 83
(-3x + 2x2) + -3(5 + -1x) = 83
-3x + 2x2 + (5 * -3 + -1x * -3) = 83
-3x + 2x2 + (-15 + 3x) = 83

Reorder the terms:
-15 + -3x + 3x + 2x2 = 83

Combine like terms: -3x + 3x = 0
-15 + 0 + 2x2 = 83
-15 + 2x2 = 83

Solving
-15 + 2x2 = 83

Solving for variable 'x'.

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

Add '15' to each side of the equation.
-15 + 15 + 2x2 = 83 + 15

Combine like terms: -15 + 15 = 0
0 + 2x2 = 83 + 15
2x2 = 83 + 15

Combine like terms: 83 + 15 = 98
2x2 = 98

Divide each side by '2'.
x2 = 49

Simplifying
x2 = 49

Take the square root of each side:
x = {-7, 7}