3t^2+21t=18

Solution for 3t^2+21t=18 equation:

Simplifying
3t2 + 21t = 18

Reorder the terms:
21t + 3t2 = 18

Solving
21t + 3t2 = 18

Solving for variable 't'.

Reorder the terms:
-18 + 21t + 3t2 = 18 + -18

Combine like terms: 18 + -18 = 0
-18 + 21t + 3t2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-6 + 7t + t2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-6 + 7t + t2)' equal to zero and attempt to solve:

Simplifying
-6 + 7t + t2 = 0

Solving
-6 + 7t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 7t + 6 + t2 = 0 + 6

Reorder the terms:
-6 + 6 + 7t + t2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 7t + t2 = 0 + 6
7t + t2 = 0 + 6

Combine like terms: 0 + 6 = 6
7t + t2 = 6

The t term is 7t.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7t + 12.25 + t2 = 6 + 12.25

Reorder the terms:
12.25 + 7t + t2 = 6 + 12.25

Combine like terms: 6 + 12.25 = 18.25
12.25 + 7t + t2 = 18.25

Factor a perfect square on the left side:
(t + 3.5)(t + 3.5) = 18.25

Calculate the square root of the right side: 4.272001873

Break this problem into two subproblems by setting 
(t + 3.5) equal to 4.272001873 and -4.272001873.

Subproblem 1
t + 3.5 = 4.272001873

Simplifying
t + 3.5 = 4.272001873

Reorder the terms:
3.5 + t = 4.272001873

Solving
3.5 + t = 4.272001873

Solving for variable 't'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + t = 4.272001873 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + t = 4.272001873 + -3.5
t = 4.272001873 + -3.5

Combine like terms: 4.272001873 + -3.5 = 0.772001873
t = 0.772001873

Simplifying
t = 0.772001873

Subproblem 2
t + 3.5 = -4.272001873

Simplifying
t + 3.5 = -4.272001873

Reorder the terms:
3.5 + t = -4.272001873

Solving
3.5 + t = -4.272001873

Solving for variable 't'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + t = -4.272001873 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + t = -4.272001873 + -3.5
t = -4.272001873 + -3.5

Combine like terms: -4.272001873 + -3.5 = -7.772001873
t = -7.772001873

Simplifying
t = -7.772001873

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.772001873, -7.772001873}
Solution
t = {0.772001873, -7.772001873}