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

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

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

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

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

Solving
3t + t2 = 3 + 3t2

Solving for variable 't'.

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

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

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

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

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

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

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

Move the constant term to the right:

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

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

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -1.5t + t2 = 0 + -1.5
-1.5t + t2 = 0 + -1.5

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

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 = -1.5 + 0.5625

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

Combine like terms: -1.5 + 0.5625 = -0.9375
0.5625 + -1.5t + t2 = -0.9375

Factor a perfect square on the left side:
(t + -0.75)(t + -0.75) = -0.9375

Can't calculate square root of the right side.

The solution to this equation could not be determined.