2t(t+5)+1=3t-3-t^2

Solution for 2t(t+5)+1=3t-3-t^2 equation:

Simplifying
2t(t + 5) + 1 = 3t + -3 + -1t2

Reorder the terms:
2t(5 + t) + 1 = 3t + -3 + -1t2
(5 * 2t + t * 2t) + 1 = 3t + -3 + -1t2
(10t + 2t2) + 1 = 3t + -3 + -1t2

Reorder the terms:
1 + 10t + 2t2 = 3t + -3 + -1t2

Reorder the terms:
1 + 10t + 2t2 = -3 + 3t + -1t2

Solving
1 + 10t + 2t2 = -3 + 3t + -1t2

Solving for variable 't'.

Reorder the terms:
1 + 3 + 10t + -3t + 2t2 + t2 = -3 + 3t + -1t2 + 3 + -3t + t2

Combine like terms: 1 + 3 = 4
4 + 10t + -3t + 2t2 + t2 = -3 + 3t + -1t2 + 3 + -3t + t2

Combine like terms: 10t + -3t = 7t
4 + 7t + 2t2 + t2 = -3 + 3t + -1t2 + 3 + -3t + t2

Combine like terms: 2t2 + t2 = 3t2
4 + 7t + 3t2 = -3 + 3t + -1t2 + 3 + -3t + t2

Reorder the terms:
4 + 7t + 3t2 = -3 + 3 + 3t + -3t + -1t2 + t2

Combine like terms: -3 + 3 = 0
4 + 7t + 3t2 = 0 + 3t + -3t + -1t2 + t2
4 + 7t + 3t2 = 3t + -3t + -1t2 + t2

Combine like terms: 3t + -3t = 0
4 + 7t + 3t2 = 0 + -1t2 + t2
4 + 7t + 3t2 = -1t2 + t2

Combine like terms: -1t2 + t2 = 0
4 + 7t + 3t2 = 0

Factor a trinomial.
(4 + 3t)(1 + t) = 0

Subproblem 1
Set the factor '(4 + 3t)' equal to zero and attempt to solve:

Simplifying
4 + 3t = 0

Solving
4 + 3t = 0

Move all terms containing t to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + 3t = 0 + -4

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

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

Divide each side by '3'.
t = -1.333333333

Simplifying
t = -1.333333333
Subproblem 2
Set the factor '(1 + t)' equal to zero and attempt to solve:

Simplifying
1 + t = 0

Solving
1 + t = 0

Move all terms containing t to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + t = 0 + -1
t = 0 + -1

Combine like terms: 0 + -1 = -1
t = -1

Simplifying
t = -1
Solution
t = {-1.333333333, -1}