300=420t(2-t)

Solution for 300=420t(2-t) equation:

Simplifying
300 = 420t(2 + -1t)
300 = (2 * 420t + -1t * 420t)
300 = (840t + -420t2)

Solving
300 = 840t + -420t2

Solving for variable 't'.

Reorder the terms:
300 + -840t + 420t2 = 840t + -840t + -420t2 + 420t2

Combine like terms: 840t + -840t = 0
300 + -840t + 420t2 = 0 + -420t2 + 420t2
300 + -840t + 420t2 = -420t2 + 420t2

Combine like terms: -420t2 + 420t2 = 0
300 + -840t + 420t2 = 0

Factor out the Greatest Common Factor (GCF), '60'.
60(5 + -14t + 7t2) = 0

Ignore the factor 60.
Subproblem 1
Set the factor '(5 + -14t + 7t2)' equal to zero and attempt to solve:

Simplifying
5 + -14t + 7t2 = 0

Solving
5 + -14t + 7t2 = 0

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

Divide each side by '7'.
0.7142857143 + -2t + t2 = 0

Move the constant term to the right:

Add '-0.7142857143' to each side of the equation.
0.7142857143 + -2t + -0.7142857143 + t2 = 0 + -0.7142857143

Reorder the terms:
0.7142857143 + -0.7142857143 + -2t + t2 = 0 + -0.7142857143

Combine like terms: 0.7142857143 + -0.7142857143 = 0.0000000000
0.0000000000 + -2t + t2 = 0 + -0.7142857143
-2t + t2 = 0 + -0.7142857143

Combine like terms: 0 + -0.7142857143 = -0.7142857143
-2t + t2 = -0.7142857143

The t term is -2t.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2t + 1 + t2 = -0.7142857143 + 1

Reorder the terms:
1 + -2t + t2 = -0.7142857143 + 1

Combine like terms: -0.7142857143 + 1 = 0.2857142857
1 + -2t + t2 = 0.2857142857

Factor a perfect square on the left side:
(t + -1)(t + -1) = 0.2857142857

Calculate the square root of the right side: 0.534522484

Break this problem into two subproblems by setting 
(t + -1) equal to 0.534522484 and -0.534522484.

Subproblem 1
t + -1 = 0.534522484

Simplifying
t + -1 = 0.534522484

Reorder the terms:
-1 + t = 0.534522484

Solving
-1 + t = 0.534522484

Solving for variable 't'.

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

Add '1' to each side of the equation.
-1 + 1 + t = 0.534522484 + 1

Combine like terms: -1 + 1 = 0
0 + t = 0.534522484 + 1
t = 0.534522484 + 1

Combine like terms: 0.534522484 + 1 = 1.534522484
t = 1.534522484

Simplifying
t = 1.534522484

Subproblem 2
t + -1 = -0.534522484

Simplifying
t + -1 = -0.534522484

Reorder the terms:
-1 + t = -0.534522484

Solving
-1 + t = -0.534522484

Solving for variable 't'.

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

Add '1' to each side of the equation.
-1 + 1 + t = -0.534522484 + 1

Combine like terms: -1 + 1 = 0
0 + t = -0.534522484 + 1
t = -0.534522484 + 1

Combine like terms: -0.534522484 + 1 = 0.465477516
t = 0.465477516

Simplifying
t = 0.465477516

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.534522484, 0.465477516}
Solution
t = {1.534522484, 0.465477516}