156t-16t^2=60

Simple and best practice solution for 156t-16t^2=60 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for 156t-16t^2=60 equation: 


Simplifying
156t + -16t2 = 60

Solving
156t + -16t2 = 60

Solving for variable 't'.

Reorder the terms:
-60 + 156t + -16t2 = 60 + -60

Combine like terms: 60 + -60 = 0
-60 + 156t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-15 + 39t + -4t2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-15 + 39t + -4t2)' equal to zero and attempt to solve:

Simplifying
-15 + 39t + -4t2 = 0

Solving
-15 + 39t + -4t2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
3.75 + -9.75t + t2 = 0

Move the constant term to the right:

Add '-3.75' to each side of the equation.
3.75 + -9.75t + -3.75 + t2 = 0 + -3.75

Reorder the terms:
3.75 + -3.75 + -9.75t + t2 = 0 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + -9.75t + t2 = 0 + -3.75
-9.75t + t2 = 0 + -3.75

Combine like terms: 0 + -3.75 = -3.75
-9.75t + t2 = -3.75

The t term is -9.75t.  Take half its coefficient (-4.875).
Square it (23.765625) and add it to both sides.

Add '23.765625' to each side of the equation.
-9.75t + 23.765625 + t2 = -3.75 + 23.765625

Reorder the terms:
23.765625 + -9.75t + t2 = -3.75 + 23.765625

Combine like terms: -3.75 + 23.765625 = 20.015625
23.765625 + -9.75t + t2 = 20.015625

Factor a perfect square on the left side:
(t + -4.875)(t + -4.875) = 20.015625

Calculate the square root of the right side: 4.473882542

Break this problem into two subproblems by setting 
(t + -4.875) equal to 4.473882542 and -4.473882542.


Subproblem 1
t + -4.875 = 4.473882542

Simplifying
t + -4.875 = 4.473882542

Reorder the terms:
-4.875 + t = 4.473882542

Solving
-4.875 + t = 4.473882542

Solving for variable 't'.

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

Add '4.875' to each side of the equation.
-4.875 + 4.875 + t = 4.473882542 + 4.875

Combine like terms: -4.875 + 4.875 = 0.000
0.000 + t = 4.473882542 + 4.875
t = 4.473882542 + 4.875

Combine like terms: 4.473882542 + 4.875 = 9.348882542
t = 9.348882542

Simplifying
t = 9.348882542


Subproblem 2
t + -4.875 = -4.473882542

Simplifying
t + -4.875 = -4.473882542

Reorder the terms:
-4.875 + t = -4.473882542

Solving
-4.875 + t = -4.473882542

Solving for variable 't'.

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

Add '4.875' to each side of the equation.
-4.875 + 4.875 + t = -4.473882542 + 4.875

Combine like terms: -4.875 + 4.875 = 0.000
0.000 + t = -4.473882542 + 4.875
t = -4.473882542 + 4.875

Combine like terms: -4.473882542 + 4.875 = 0.401117458
t = 0.401117458

Simplifying
t = 0.401117458


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {9.348882542, 0.401117458}
Solution
t = {9.348882542, 0.401117458}

See similar equations:

| 22n-21n-14=-21 | | 2x+24=3(2x+1) | | -8(-10)-7= | | 3(d-8)-5=(9d+2)+1 | | -2y=-48 | | 47=-8x | | 21+d=-16 | | -5t^2+5t+2=3 | | 4x+5=-4x+16 | | -154=6(1-7m)+2m | | -5t^2+5t+2=0 | | 26x=182 | | 3(y+2)-5=13 | | 3-(6x-22)=7(x-3) | | 47/9= | | 11-(x+7)=9x-6 | | -0.6=6.5n-5.5n+0.9 | | 21y=189 | | 8/1.5= | | 0.5y+4.1=5.7-0.3y | | 450=(n*2-5)*18 | | x-4.1=4.6 | | 17x=170 | | 8/1.8= | | 62=-15+-8x | | 2x-12+x+30=180 | | -1=-7p-12+8p | | 2+5t-5t^2=0 | | 179-(7x+11)=7(x+9)+x | | 62=-15-8x | | 3x+17=5x-15 | | -49.3/(-4.2)= |

Equations solver categories