16t^2+60t-40=0

Simple and best practice solution for 16t^2+60t-40=0 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 16t^2+60t-40=0 equation: 


Simplifying
16t2 + 60t + -40 = 0

Reorder the terms:
-40 + 60t + 16t2 = 0

Solving
-40 + 60t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-10 + 15t + 4t2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-10 + 15t + 4t2)' equal to zero and attempt to solve:

Simplifying
-10 + 15t + 4t2 = 0

Solving
-10 + 15t + 4t2 = 0

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

Divide each side by '4'.
-2.5 + 3.75t + t2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 3.75t + 2.5 + t2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 3.75t + t2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 3.75t + t2 = 0 + 2.5
3.75t + t2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
3.75t + t2 = 2.5

The t term is 3.75t.  Take half its coefficient (1.875).
Square it (3.515625) and add it to both sides.

Add '3.515625' to each side of the equation.
3.75t + 3.515625 + t2 = 2.5 + 3.515625

Reorder the terms:
3.515625 + 3.75t + t2 = 2.5 + 3.515625

Combine like terms: 2.5 + 3.515625 = 6.015625
3.515625 + 3.75t + t2 = 6.015625

Factor a perfect square on the left side:
(t + 1.875)(t + 1.875) = 6.015625

Calculate the square root of the right side: 2.452677109

Break this problem into two subproblems by setting 
(t + 1.875) equal to 2.452677109 and -2.452677109.


Subproblem 1
t + 1.875 = 2.452677109

Simplifying
t + 1.875 = 2.452677109

Reorder the terms:
1.875 + t = 2.452677109

Solving
1.875 + t = 2.452677109

Solving for variable 't'.

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

Add '-1.875' to each side of the equation.
1.875 + -1.875 + t = 2.452677109 + -1.875

Combine like terms: 1.875 + -1.875 = 0.000
0.000 + t = 2.452677109 + -1.875
t = 2.452677109 + -1.875

Combine like terms: 2.452677109 + -1.875 = 0.577677109
t = 0.577677109

Simplifying
t = 0.577677109


Subproblem 2
t + 1.875 = -2.452677109

Simplifying
t + 1.875 = -2.452677109

Reorder the terms:
1.875 + t = -2.452677109

Solving
1.875 + t = -2.452677109

Solving for variable 't'.

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

Add '-1.875' to each side of the equation.
1.875 + -1.875 + t = -2.452677109 + -1.875

Combine like terms: 1.875 + -1.875 = 0.000
0.000 + t = -2.452677109 + -1.875
t = -2.452677109 + -1.875

Combine like terms: -2.452677109 + -1.875 = -4.327677109
t = -4.327677109

Simplifying
t = -4.327677109


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.577677109, -4.327677109}
Solution
t = {0.577677109, -4.327677109}

See similar equations:

| 3(x-7)-7x=15 | | B=4(25)-9square | | ax-5=15 | | 112+-18= | | 7.5x=75 | | 1x-9y=11 | | 3x+2x=4(2x+12) | | 22.5x=180 | | 4-5=15 | | 18+35-18= | | -3x+5=-1-4x | | 4.5x=81 | | 3x(3-x)-(4-x)3x=0 | | 12.5x=250 | | 6x=35333 | | 7x+23=x+65 | | 5(t)=1 | | 4m(m+3)=0 | | 3(x-1)+5x= | | 3x^2-3x-70=0 | | 4(x+2)+3= | | x+39=4x+18 | | log(8)(2x+3)=6 | | -25=7(x-7) | | 3(7x-3)= | | 4x^2-100=2 | | 8(x-4)=-64 | | 0.66n+0.33=-0.33 | | (x^3)-(3.2x^2)+2x+5=0 | | 16-7a=3a+2 | | 6x^2+60x=-54 | | (3r-5)(r-7)=0 |

Equations solver categories