t^2-t=3t-21

Solution for t^2-t=3t-21 equation:

Simplifying
t2 + -1t = 3t + -21

Reorder the terms:
-1t + t2 = 3t + -21

Reorder the terms:
-1t + t2 = -21 + 3t

Solving
-1t + t2 = -21 + 3t

Solving for variable 't'.

Reorder the terms:
21 + -1t + -3t + t2 = -21 + 3t + 21 + -3t

Combine like terms: -1t + -3t = -4t
21 + -4t + t2 = -21 + 3t + 21 + -3t

Reorder the terms:
21 + -4t + t2 = -21 + 21 + 3t + -3t

Combine like terms: -21 + 21 = 0
21 + -4t + t2 = 0 + 3t + -3t
21 + -4t + t2 = 3t + -3t

Combine like terms: 3t + -3t = 0
21 + -4t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-21' to each side of the equation.
21 + -4t + -21 + t2 = 0 + -21

Reorder the terms:
21 + -21 + -4t + t2 = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -4t + t2 = 0 + -21
-4t + t2 = 0 + -21

Combine like terms: 0 + -21 = -21
-4t + t2 = -21

The t term is -4t.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4t + 4 + t2 = -21 + 4

Reorder the terms:
4 + -4t + t2 = -21 + 4

Combine like terms: -21 + 4 = -17
4 + -4t + t2 = -17

Factor a perfect square on the left side:
(t + -2)(t + -2) = -17

Can't calculate square root of the right side.

The solution to this equation could not be determined.