3t^2+3t=105

Solution for 3t^2+3t=105 equation:

Simplifying
3t2 + 3t = 105

Reorder the terms:
3t + 3t2 = 105

Solving
3t + 3t2 = 105

Solving for variable 't'.

Reorder the terms:
-105 + 3t + 3t2 = 105 + -105

Combine like terms: 105 + -105 = 0
-105 + 3t + 3t2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-35 + t + t2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-35 + t + t2)' equal to zero and attempt to solve:

Simplifying
-35 + t + t2 = 0

Solving
-35 + t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '35' to each side of the equation.
-35 + t + 35 + t2 = 0 + 35

Reorder the terms:
-35 + 35 + t + t2 = 0 + 35

Combine like terms: -35 + 35 = 0
0 + t + t2 = 0 + 35
t + t2 = 0 + 35

Combine like terms: 0 + 35 = 35
t + t2 = 35

The t term is t.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
t + 0.25 + t2 = 35 + 0.25

Reorder the terms:
0.25 + t + t2 = 35 + 0.25

Combine like terms: 35 + 0.25 = 35.25
0.25 + t + t2 = 35.25

Factor a perfect square on the left side:
(t + 0.5)(t + 0.5) = 35.25

Calculate the square root of the right side: 5.937171044

Break this problem into two subproblems by setting 
(t + 0.5) equal to 5.937171044 and -5.937171044.

Subproblem 1
t + 0.5 = 5.937171044

Simplifying
t + 0.5 = 5.937171044

Reorder the terms:
0.5 + t = 5.937171044

Solving
0.5 + t = 5.937171044

Solving for variable 't'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + t = 5.937171044 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = 5.937171044 + -0.5
t = 5.937171044 + -0.5

Combine like terms: 5.937171044 + -0.5 = 5.437171044
t = 5.437171044

Simplifying
t = 5.437171044

Subproblem 2
t + 0.5 = -5.937171044

Simplifying
t + 0.5 = -5.937171044

Reorder the terms:
0.5 + t = -5.937171044

Solving
0.5 + t = -5.937171044

Solving for variable 't'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + t = -5.937171044 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = -5.937171044 + -0.5
t = -5.937171044 + -0.5

Combine like terms: -5.937171044 + -0.5 = -6.437171044
t = -6.437171044

Simplifying
t = -6.437171044

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {5.437171044, -6.437171044}
Solution
t = {5.437171044, -6.437171044}