-64=6t-4t^2

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Solution for -64=6t-4t^2 equation: 


Simplifying
-64 = 6t + -4t2

Solving
-64 = 6t + -4t2

Solving for variable 't'.

Reorder the terms:
-64 + -6t + 4t2 = 6t + -6t + -4t2 + 4t2

Combine like terms: 6t + -6t = 0
-64 + -6t + 4t2 = 0 + -4t2 + 4t2
-64 + -6t + 4t2 = -4t2 + 4t2

Combine like terms: -4t2 + 4t2 = 0
-64 + -6t + 4t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-32 + -3t + 2t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-32 + -3t + 2t2)' equal to zero and attempt to solve:

Simplifying
-32 + -3t + 2t2 = 0

Solving
-32 + -3t + 2t2 = 0

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

Divide each side by '2'.
-16 + -1.5t + t2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -1.5t + 16 + t2 = 0 + 16

Reorder the terms:
-16 + 16 + -1.5t + t2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -1.5t + t2 = 0 + 16
-1.5t + t2 = 0 + 16

Combine like terms: 0 + 16 = 16
-1.5t + t2 = 16

The t term is -1.5t.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5t + 0.5625 + t2 = 16 + 0.5625

Reorder the terms:
0.5625 + -1.5t + t2 = 16 + 0.5625

Combine like terms: 16 + 0.5625 = 16.5625
0.5625 + -1.5t + t2 = 16.5625

Factor a perfect square on the left side:
(t + -0.75)(t + -0.75) = 16.5625

Calculate the square root of the right side: 4.069705149

Break this problem into two subproblems by setting 
(t + -0.75) equal to 4.069705149 and -4.069705149.


Subproblem 1
t + -0.75 = 4.069705149

Simplifying
t + -0.75 = 4.069705149

Reorder the terms:
-0.75 + t = 4.069705149

Solving
-0.75 + t = 4.069705149

Solving for variable 't'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + t = 4.069705149 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + t = 4.069705149 + 0.75
t = 4.069705149 + 0.75

Combine like terms: 4.069705149 + 0.75 = 4.819705149
t = 4.819705149

Simplifying
t = 4.819705149


Subproblem 2
t + -0.75 = -4.069705149

Simplifying
t + -0.75 = -4.069705149

Reorder the terms:
-0.75 + t = -4.069705149

Solving
-0.75 + t = -4.069705149

Solving for variable 't'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + t = -4.069705149 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + t = -4.069705149 + 0.75
t = -4.069705149 + 0.75

Combine like terms: -4.069705149 + 0.75 = -3.319705149
t = -3.319705149

Simplifying
t = -3.319705149


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.819705149, -3.319705149}
Solution
t = {4.819705149, -3.319705149}

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