2+t(3-t)-3t=0

Solution for 2+t(3-t)-3t=0 equation:

Simplifying
2 + t(3 + -1t) + -3t = 0
2 + (3 * t + -1t * t) + -3t = 0
2 + (3t + -1t2) + -3t = 0

Reorder the terms:
2 + 3t + -3t + -1t2 = 0

Combine like terms: 3t + -3t = 0
2 + 0 + -1t2 = 0
2 + -1t2 = 0

Solving
2 + -1t2 = 0

Solving for variable 't'.

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

Add '-2' to each side of the equation.
2 + -2 + -1t2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1t2 = 0 + -2
-1t2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1t2 = -2

Divide each side by '-1'.
t2 = 2

Simplifying
t2 = 2

Take the square root of each side:
t = {-1.414213562, 1.414213562}