2x(x-1)+2(x-3)=3

Solution for 2x(x-1)+2(x-3)=3 equation:

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

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

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

Reorder the terms:
-6 + -2x + 2x + 2x2 = 3

Combine like terms: -2x + 2x = 0
-6 + 0 + 2x2 = 3
-6 + 2x2 = 3

Solving
-6 + 2x2 = 3

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + 2x2 = 3 + 6

Combine like terms: -6 + 6 = 0
0 + 2x2 = 3 + 6
2x2 = 3 + 6

Combine like terms: 3 + 6 = 9
2x2 = 9

Divide each side by '2'.
x2 = 4.5

Simplifying
x2 = 4.5

Take the square root of each side:
x = {-2.121320344, 2.121320344}