110=t(80-5t)

Simple and best practice solution for 110=t(80-5t) 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 110=t(80-5t) equation: 


Simplifying
110 = t(80 + -5t)
110 = (80 * t + -5t * t)
110 = (80t + -5t2)

Solving
110 = 80t + -5t2

Solving for variable 't'.

Reorder the terms:
110 + -80t + 5t2 = 80t + -80t + -5t2 + 5t2

Combine like terms: 80t + -80t = 0
110 + -80t + 5t2 = 0 + -5t2 + 5t2
110 + -80t + 5t2 = -5t2 + 5t2

Combine like terms: -5t2 + 5t2 = 0
110 + -80t + 5t2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(22 + -16t + t2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(22 + -16t + t2)' equal to zero and attempt to solve:

Simplifying
22 + -16t + t2 = 0

Solving
22 + -16t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-22' to each side of the equation.
22 + -16t + -22 + t2 = 0 + -22

Reorder the terms:
22 + -22 + -16t + t2 = 0 + -22

Combine like terms: 22 + -22 = 0
0 + -16t + t2 = 0 + -22
-16t + t2 = 0 + -22

Combine like terms: 0 + -22 = -22
-16t + t2 = -22

The t term is -16t.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16t + 64 + t2 = -22 + 64

Reorder the terms:
64 + -16t + t2 = -22 + 64

Combine like terms: -22 + 64 = 42
64 + -16t + t2 = 42

Factor a perfect square on the left side:
(t + -8)(t + -8) = 42

Calculate the square root of the right side: 6.480740698

Break this problem into two subproblems by setting 
(t + -8) equal to 6.480740698 and -6.480740698.


Subproblem 1
t + -8 = 6.480740698

Simplifying
t + -8 = 6.480740698

Reorder the terms:
-8 + t = 6.480740698

Solving
-8 + t = 6.480740698

Solving for variable 't'.

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

Add '8' to each side of the equation.
-8 + 8 + t = 6.480740698 + 8

Combine like terms: -8 + 8 = 0
0 + t = 6.480740698 + 8
t = 6.480740698 + 8

Combine like terms: 6.480740698 + 8 = 14.480740698
t = 14.480740698

Simplifying
t = 14.480740698


Subproblem 2
t + -8 = -6.480740698

Simplifying
t + -8 = -6.480740698

Reorder the terms:
-8 + t = -6.480740698

Solving
-8 + t = -6.480740698

Solving for variable 't'.

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

Add '8' to each side of the equation.
-8 + 8 + t = -6.480740698 + 8

Combine like terms: -8 + 8 = 0
0 + t = -6.480740698 + 8
t = -6.480740698 + 8

Combine like terms: -6.480740698 + 8 = 1.519259302
t = 1.519259302

Simplifying
t = 1.519259302


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {14.480740698, 1.519259302}
Solution
t = {14.480740698, 1.519259302}

See similar equations:

| -7-4w=13 | | 1/2x*17 | | 5(3x-2)=55 | | 42x-14= | | 0.125x^2+30x=15x-200 | | 21+19m=42+12m | | x/41=-12+3 | | -4x-9-4x=71 | | 150m-75m+48000=50500-175m | | 32-3= | | 7(x+6)=9x+3-2x+39 | | x-(-1.5)=-9 | | 8+x+3x=8 | | 24/16 | | 5g+9=2g+15-15 | | e^2+3e-24=0 | | -58-9x=50+3x | | 4v+8=92 | | 1/2x+5=4 | | x^6=16x^2 | | 150m-100m+46125=43200-175m | | x-(-1.5)=9 | | 20x+8=4(2x+8) | | .5(x+100)=.56x-418 | | 7x+1-6x=8 | | -5/6y-(y-1/2)=1/24(y-9) | | 22w+40=18w | | 23x-8-14x=11 | | 0.125x^2+30x=15x+200 | | 4(2a-2)=-10(a+5) | | 30x=50+4x^2 | | (4+x)-3=6 |

Equations solver categories