3t=8+(3t+2)(t-1)

Solution for 3t=8+(3t+2)(t-1) equation:

Simplifying
3t = 8 + (3t + 2)(t + -1)

Reorder the terms:
3t = 8 + (2 + 3t)(t + -1)

Reorder the terms:
3t = 8 + (2 + 3t)(-1 + t)

Multiply (2 + 3t) * (-1 + t)
3t = 8 + (2(-1 + t) + 3t * (-1 + t))
3t = 8 + ((-1 * 2 + t * 2) + 3t * (-1 + t))
3t = 8 + ((-2 + 2t) + 3t * (-1 + t))
3t = 8 + (-2 + 2t + (-1 * 3t + t * 3t))
3t = 8 + (-2 + 2t + (-3t + 3t2))

Combine like terms: 2t + -3t = -1t
3t = 8 + (-2 + -1t + 3t2)

Combine like terms: 8 + -2 = 6
3t = 6 + -1t + 3t2

Solving
3t = 6 + -1t + 3t2

Solving for variable 't'.

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

Combine like terms: 3t + t = 4t
-6 + 4t + -3t2 = 6 + -1t + 3t2 + -6 + t + -3t2

Reorder the terms:
-6 + 4t + -3t2 = 6 + -6 + -1t + t + 3t2 + -3t2

Combine like terms: 6 + -6 = 0
-6 + 4t + -3t2 = 0 + -1t + t + 3t2 + -3t2
-6 + 4t + -3t2 = -1t + t + 3t2 + -3t2

Combine like terms: -1t + t = 0
-6 + 4t + -3t2 = 0 + 3t2 + -3t2
-6 + 4t + -3t2 = 3t2 + -3t2

Combine like terms: 3t2 + -3t2 = 0
-6 + 4t + -3t2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
2 + -1.333333333t + t2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -1.333333333t + -2 + t2 = 0 + -2

Reorder the terms:
2 + -2 + -1.333333333t + t2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1.333333333t + t2 = 0 + -2
-1.333333333t + t2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1.333333333t + t2 = -2

The t term is -1.333333333t.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333t + 0.4444444442 + t2 = -2 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333t + t2 = -2 + 0.4444444442

Combine like terms: -2 + 0.4444444442 = -1.5555555558
0.4444444442 + -1.333333333t + t2 = -1.5555555558

Factor a perfect square on the left side:
(t + -0.6666666665)(t + -0.6666666665) = -1.5555555558

Can't calculate square root of the right side.

The solution to this equation could not be determined.