12t-0.3t^2-60=0

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Solution for 12t-0.3t^2-60=0 equation:


Simplifying
12t + -0.3t2 + -60 = 0

Reorder the terms:
-60 + 12t + -0.3t2 = 0

Solving
-60 + 12t + -0.3t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
-0.3 the coefficient of the squared term: 

Divide each side by '-0.3'.
200 + -40t + t2 = 0

Move the constant term to the right:

Add '-200' to each side of the equation.
200 + -40t + -200 + t2 = 0 + -200

Reorder the terms:
200 + -200 + -40t + t2 = 0 + -200

Combine like terms: 200 + -200 = 0
0 + -40t + t2 = 0 + -200
-40t + t2 = 0 + -200

Combine like terms: 0 + -200 = -200
-40t + t2 = -200

The t term is -40t.  Take half its coefficient (-20).
Square it (400) and add it to both sides.

Add '400' to each side of the equation.
-40t + 400 + t2 = -200 + 400

Reorder the terms:
400 + -40t + t2 = -200 + 400

Combine like terms: -200 + 400 = 200
400 + -40t + t2 = 200

Factor a perfect square on the left side:
(t + -20)(t + -20) = 200

Calculate the square root of the right side: 14.142135624

Break this problem into two subproblems by setting 
(t + -20) equal to 14.142135624 and -14.142135624.

Subproblem 1

t + -20 = 14.142135624 Simplifying t + -20 = 14.142135624 Reorder the terms: -20 + t = 14.142135624 Solving -20 + t = 14.142135624 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + t = 14.142135624 + 20 Combine like terms: -20 + 20 = 0 0 + t = 14.142135624 + 20 t = 14.142135624 + 20 Combine like terms: 14.142135624 + 20 = 34.142135624 t = 34.142135624 Simplifying t = 34.142135624

Subproblem 2

t + -20 = -14.142135624 Simplifying t + -20 = -14.142135624 Reorder the terms: -20 + t = -14.142135624 Solving -20 + t = -14.142135624 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + t = -14.142135624 + 20 Combine like terms: -20 + 20 = 0 0 + t = -14.142135624 + 20 t = -14.142135624 + 20 Combine like terms: -14.142135624 + 20 = 5.857864376 t = 5.857864376 Simplifying t = 5.857864376

Solution

The solution to the problem is based on the solutions from the subproblems. t = {34.142135624, 5.857864376}

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