2t^2+3t+500=3t^2+t+300

Solution for 2t^2+3t+500=3t^2+t+300 equation:

Simplifying
2t2 + 3t + 500 = 3t2 + t + 300

Reorder the terms:
500 + 3t + 2t2 = 3t2 + t + 300

Reorder the terms:
500 + 3t + 2t2 = 300 + t + 3t2

Solving
500 + 3t + 2t2 = 300 + t + 3t2

Solving for variable 't'.

Reorder the terms:
500 + -300 + 3t + -1t + 2t2 + -3t2 = 300 + t + 3t2 + -300 + -1t + -3t2

Combine like terms: 500 + -300 = 200
200 + 3t + -1t + 2t2 + -3t2 = 300 + t + 3t2 + -300 + -1t + -3t2

Combine like terms: 3t + -1t = 2t
200 + 2t + 2t2 + -3t2 = 300 + t + 3t2 + -300 + -1t + -3t2

Combine like terms: 2t2 + -3t2 = -1t2
200 + 2t + -1t2 = 300 + t + 3t2 + -300 + -1t + -3t2

Reorder the terms:
200 + 2t + -1t2 = 300 + -300 + t + -1t + 3t2 + -3t2

Combine like terms: 300 + -300 = 0
200 + 2t + -1t2 = 0 + t + -1t + 3t2 + -3t2
200 + 2t + -1t2 = t + -1t + 3t2 + -3t2

Combine like terms: t + -1t = 0
200 + 2t + -1t2 = 0 + 3t2 + -3t2
200 + 2t + -1t2 = 3t2 + -3t2

Combine like terms: 3t2 + -3t2 = 0
200 + 2t + -1t2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-200 + -2t + t2 = 0

Move the constant term to the right:

Add '200' to each side of the equation.
-200 + -2t + 200 + t2 = 0 + 200

Reorder the terms:
-200 + 200 + -2t + t2 = 0 + 200

Combine like terms: -200 + 200 = 0
0 + -2t + t2 = 0 + 200
-2t + t2 = 0 + 200

Combine like terms: 0 + 200 = 200
-2t + t2 = 200

The t term is -2t.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2t + 1 + t2 = 200 + 1

Reorder the terms:
1 + -2t + t2 = 200 + 1

Combine like terms: 200 + 1 = 201
1 + -2t + t2 = 201

Factor a perfect square on the left side:
(t + -1)(t + -1) = 201

Calculate the square root of the right side: 14.177446879

Break this problem into two subproblems by setting 
(t + -1) equal to 14.177446879 and -14.177446879.

Subproblem 1
t + -1 = 14.177446879

Simplifying
t + -1 = 14.177446879

Reorder the terms:
-1 + t = 14.177446879

Solving
-1 + t = 14.177446879

Solving for variable 't'.

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 = 14.177446879 + 1

Combine like terms: -1 + 1 = 0
0 + t = 14.177446879 + 1
t = 14.177446879 + 1

Combine like terms: 14.177446879 + 1 = 15.177446879
t = 15.177446879

Simplifying
t = 15.177446879

Subproblem 2
t + -1 = -14.177446879

Simplifying
t + -1 = -14.177446879

Reorder the terms:
-1 + t = -14.177446879

Solving
-1 + t = -14.177446879

Solving for variable 't'.

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 = -14.177446879 + 1

Combine like terms: -1 + 1 = 0
0 + t = -14.177446879 + 1
t = -14.177446879 + 1

Combine like terms: -14.177446879 + 1 = -13.177446879
t = -13.177446879

Simplifying
t = -13.177446879

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {15.177446879, -13.177446879}