2(t^2-3t-7)+21=0

Solution for 2(t^2-3t-7)+21=0 equation:

Simplifying
2(t2 + -3t + -7) + 21 = 0

Reorder the terms:
2(-7 + -3t + t2) + 21 = 0
(-7 * 2 + -3t * 2 + t2 * 2) + 21 = 0
(-14 + -6t + 2t2) + 21 = 0

Reorder the terms:
-14 + 21 + -6t + 2t2 = 0

Combine like terms: -14 + 21 = 7
7 + -6t + 2t2 = 0

Solving
7 + -6t + 2t2 = 0

Solving for variable 't'.

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

Divide each side by '2'.
3.5 + -3t + t2 = 0

Move the constant term to the right:

Add '-3.5' to each side of the equation.
3.5 + -3t + -3.5 + t2 = 0 + -3.5

Reorder the terms:
3.5 + -3.5 + -3t + t2 = 0 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + -3t + t2 = 0 + -3.5
-3t + t2 = 0 + -3.5

Combine like terms: 0 + -3.5 = -3.5
-3t + t2 = -3.5

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 = -3.5 + 2.25

Reorder the terms:
2.25 + -3t + t2 = -3.5 + 2.25

Combine like terms: -3.5 + 2.25 = -1.25
2.25 + -3t + t2 = -1.25

Factor a perfect square on the left side:
(t + -1.5)(t + -1.5) = -1.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.