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

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

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

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

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

Solving
3t + t2 = 6 + 3t2

Solving for variable 't'.

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

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

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

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

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

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
3 + -1.5t + t2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -1.5t + -3 + t2 = 0 + -3

Reorder the terms:
3 + -3 + -1.5t + t2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1.5t + t2 = 0 + -3
-1.5t + t2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1.5t + t2 = -3

The t term is -1.5t.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5t + 0.5625 + t2 = -3 + 0.5625

Reorder the terms:
0.5625 + -1.5t + t2 = -3 + 0.5625

Combine like terms: -3 + 0.5625 = -2.4375
0.5625 + -1.5t + t2 = -2.4375

Factor a perfect square on the left side:
(t + -0.75)(t + -0.75) = -2.4375

Can't calculate square root of the right side.

The solution to this equation could not be determined.