-15t^2+105t+10=0

Simple and best practice solution for -15t^2+105t+10=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 -15t^2+105t+10=0 equation: 


Simplifying
-15t2 + 105t + 10 = 0

Reorder the terms:
10 + 105t + -15t2 = 0

Solving
10 + 105t + -15t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '5'.
5(2 + 21t + -3t2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(2 + 21t + -3t2)' equal to zero and attempt to solve:

Simplifying
2 + 21t + -3t2 = 0

Solving
2 + 21t + -3t2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-0.6666666667 + -7t + t2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + -7t + 0.6666666667 + t2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + -7t + t2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + -7t + t2 = 0 + 0.6666666667
-7t + t2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
-7t + t2 = 0.6666666667

The t term is -7t.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7t + 12.25 + t2 = 0.6666666667 + 12.25

Reorder the terms:
12.25 + -7t + t2 = 0.6666666667 + 12.25

Combine like terms: 0.6666666667 + 12.25 = 12.9166666667
12.25 + -7t + t2 = 12.9166666667

Factor a perfect square on the left side:
(t + -3.5)(t + -3.5) = 12.9166666667

Calculate the square root of the right side: 3.593976442

Break this problem into two subproblems by setting 
(t + -3.5) equal to 3.593976442 and -3.593976442.


Subproblem 1
t + -3.5 = 3.593976442

Simplifying
t + -3.5 = 3.593976442

Reorder the terms:
-3.5 + t = 3.593976442

Solving
-3.5 + t = 3.593976442

Solving for variable 't'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + t = 3.593976442 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + t = 3.593976442 + 3.5
t = 3.593976442 + 3.5

Combine like terms: 3.593976442 + 3.5 = 7.093976442
t = 7.093976442

Simplifying
t = 7.093976442


Subproblem 2
t + -3.5 = -3.593976442

Simplifying
t + -3.5 = -3.593976442

Reorder the terms:
-3.5 + t = -3.593976442

Solving
-3.5 + t = -3.593976442

Solving for variable 't'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + t = -3.593976442 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + t = -3.593976442 + 3.5
t = -3.593976442 + 3.5

Combine like terms: -3.593976442 + 3.5 = -0.093976442
t = -0.093976442

Simplifying
t = -0.093976442


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {7.093976442, -0.093976442}
Solution
t = {7.093976442, -0.093976442}

See similar equations:

| x^2+2x+13=12 | | 22+x=-15 | | (x+9)[2]=-4 | | 23+11-2c=12-2c | | 8.1+3.8h+5.6h=-5 | | 2m=-6(2)-5(2) | | 24-27=-3x | | x*2+9=81 | | x-2=-[7-x] | | 5x+10-2x-3+2+4x=0 | | 40x-8y=7 | | 24-27=-3 | | 24+27=-3 | | 5(x+7)[x]2=90 | | -3+1=-9 | | 2(0.3r+1)=23-0.6 | | 2(5x+9)-4x=6x+18 | | 63m=63 | | -5=3x-x+5 | | 2m=-6(2) | | 5(x^2-1)-24x=0 | | m-3x=2x+9 | | -44=-6x-3x+10 | | -15t^2+150t-315=0 | | sr-t=us+t | | 18x^2+7X-8=0 | | 1.5-0.04X=-0.9 | | 11(10)+7= | | 238=21-v | | 2x(2x)-4= | | x(9x+18)=4x^2-6x+5 | | -2(3x+5)-4(3-x)=12 |

Equations solver categories