4.9(8t-t^2+20)=0

Solution for 4.9(8t-t^2+20)=0 equation:

Simplifying
4.9(8t + -1t2 + 20) = 0

Reorder the terms:
4.9(20 + 8t + -1t2) = 0
(20 * 4.9 + 8t * 4.9 + -1t2 * 4.9) = 0
(98 + 39.2t + -4.9t2) = 0

Solving
98 + 39.2t + -4.9t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
-4.9 the coefficient of the squared term: 

Divide each side by '-4.9'.
-20 + -8t + t2 = 0

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + -8t + 20 + t2 = 0 + 20

Reorder the terms:
-20 + 20 + -8t + t2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -8t + t2 = 0 + 20
-8t + t2 = 0 + 20

Combine like terms: 0 + 20 = 20
-8t + t2 = 20

The t term is -8t.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8t + 16 + t2 = 20 + 16

Reorder the terms:
16 + -8t + t2 = 20 + 16

Combine like terms: 20 + 16 = 36
16 + -8t + t2 = 36

Factor a perfect square on the left side:
(t + -4)(t + -4) = 36

Calculate the square root of the right side: 6

Break this problem into two subproblems by setting 
(t + -4) equal to 6 and -6.

Subproblem 1
t + -4 = 6

Simplifying
t + -4 = 6

Reorder the terms:
-4 + t = 6

Solving
-4 + t = 6

Solving for variable 't'.

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

Add '4' to each side of the equation.
-4 + 4 + t = 6 + 4

Combine like terms: -4 + 4 = 0
0 + t = 6 + 4
t = 6 + 4

Combine like terms: 6 + 4 = 10
t = 10

Simplifying
t = 10

Subproblem 2
t + -4 = -6

Simplifying
t + -4 = -6

Reorder the terms:
-4 + t = -6

Solving
-4 + t = -6

Solving for variable 't'.

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

Add '4' to each side of the equation.
-4 + 4 + t = -6 + 4

Combine like terms: -4 + 4 = 0
0 + t = -6 + 4
t = -6 + 4

Combine like terms: -6 + 4 = -2
t = -2

Simplifying
t = -2

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {10, -2}