t(t+3)=2t^2+6

Solution for t(t+3)=2t^2+6 equation:

Simplifying
t(t + 3) = 2t2 + 6

Reorder the terms:
t(3 + t) = 2t2 + 6
(3 * t + t * t) = 2t2 + 6
(3t + t2) = 2t2 + 6

Reorder the terms:
3t + t2 = 6 + 2t2

Solving
3t + t2 = 6 + 2t2

Solving for variable 't'.

Reorder the terms:
-6 + 3t + t2 + -2t2 = 6 + 2t2 + -6 + -2t2

Combine like terms: t2 + -2t2 = -1t2
-6 + 3t + -1t2 = 6 + 2t2 + -6 + -2t2

Reorder the terms:
-6 + 3t + -1t2 = 6 + -6 + 2t2 + -2t2

Combine like terms: 6 + -6 = 0
-6 + 3t + -1t2 = 0 + 2t2 + -2t2
-6 + 3t + -1t2 = 2t2 + -2t2

Combine like terms: 2t2 + -2t2 = 0
-6 + 3t + -1t2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
6 + -3t + t2 = 0

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -3t + -6 + t2 = 0 + -6

Reorder the terms:
6 + -6 + -3t + t2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -3t + t2 = 0 + -6
-3t + t2 = 0 + -6

Combine like terms: 0 + -6 = -6
-3t + t2 = -6

The t term is -3t.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3t + 2.25 + t2 = -6 + 2.25

Reorder the terms:
2.25 + -3t + t2 = -6 + 2.25

Combine like terms: -6 + 2.25 = -3.75
2.25 + -3t + t2 = -3.75

Factor a perfect square on the left side:
(t + -1.5)(t + -1.5) = -3.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.