2t^2+5t-3=3

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

Simplifying
2t2 + 5t + -3 = 3

Reorder the terms:
-3 + 5t + 2t2 = 3

Solving
-3 + 5t + 2t2 = 3

Solving for variable 't'.

Reorder the terms:
-3 + -3 + 5t + 2t2 = 3 + -3

Combine like terms: -3 + -3 = -6
-6 + 5t + 2t2 = 3 + -3

Combine like terms: 3 + -3 = 0
-6 + 5t + 2t2 = 0

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

Divide each side by '2'.
-3 + 2.5t + t2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 2.5t + 3 + t2 = 0 + 3

Reorder the terms:
-3 + 3 + 2.5t + t2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 2.5t + t2 = 0 + 3
2.5t + t2 = 0 + 3

Combine like terms: 0 + 3 = 3
2.5t + t2 = 3

The t term is 2.5t.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5t + 1.5625 + t2 = 3 + 1.5625

Reorder the terms:
1.5625 + 2.5t + t2 = 3 + 1.5625

Combine like terms: 3 + 1.5625 = 4.5625
1.5625 + 2.5t + t2 = 4.5625

Factor a perfect square on the left side:
(t + 1.25)(t + 1.25) = 4.5625

Calculate the square root of the right side: 2.136000936

Break this problem into two subproblems by setting 
(t + 1.25) equal to 2.136000936 and -2.136000936.

Subproblem 1
t + 1.25 = 2.136000936

Simplifying
t + 1.25 = 2.136000936

Reorder the terms:
1.25 + t = 2.136000936

Solving
1.25 + t = 2.136000936

Solving for variable 't'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + t = 2.136000936 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + t = 2.136000936 + -1.25
t = 2.136000936 + -1.25

Combine like terms: 2.136000936 + -1.25 = 0.886000936
t = 0.886000936

Simplifying
t = 0.886000936

Subproblem 2
t + 1.25 = -2.136000936

Simplifying
t + 1.25 = -2.136000936

Reorder the terms:
1.25 + t = -2.136000936

Solving
1.25 + t = -2.136000936

Solving for variable 't'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + t = -2.136000936 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + t = -2.136000936 + -1.25
t = -2.136000936 + -1.25

Combine like terms: -2.136000936 + -1.25 = -3.386000936
t = -3.386000936

Simplifying
t = -3.386000936

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.886000936, -3.386000936}