t(3t-7)=3

Simple and best practice solution for t(3t-7)=3 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 t(3t-7)=3 equation:


Simplifying
t(3t + -7) = 3

Reorder the terms:
t(-7 + 3t) = 3
(-7 * t + 3t * t) = 3
(-7t + 3t2) = 3

Solving
-7t + 3t2 = 3

Solving for variable 't'.

Reorder the terms:
-3 + -7t + 3t2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + -7t + 3t2 = 0

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

Divide each side by '3'.
-1 + -2.333333333t + t2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -2.333333333t + 1 + t2 = 0 + 1

Reorder the terms:
-1 + 1 + -2.333333333t + t2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2.333333333t + t2 = 0 + 1
-2.333333333t + t2 = 0 + 1

Combine like terms: 0 + 1 = 1
-2.333333333t + t2 = 1

The t term is -2.333333333t.  Take half its coefficient (-1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
-2.333333333t + 1.361111112 + t2 = 1 + 1.361111112

Reorder the terms:
1.361111112 + -2.333333333t + t2 = 1 + 1.361111112

Combine like terms: 1 + 1.361111112 = 2.361111112
1.361111112 + -2.333333333t + t2 = 2.361111112

Factor a perfect square on the left side:
(t + -1.166666667)(t + -1.166666667) = 2.361111112

Calculate the square root of the right side: 1.536590743

Break this problem into two subproblems by setting 
(t + -1.166666667) equal to 1.536590743 and -1.536590743.

Subproblem 1

t + -1.166666667 = 1.536590743 Simplifying t + -1.166666667 = 1.536590743 Reorder the terms: -1.166666667 + t = 1.536590743 Solving -1.166666667 + t = 1.536590743 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + t = 1.536590743 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + t = 1.536590743 + 1.166666667 t = 1.536590743 + 1.166666667 Combine like terms: 1.536590743 + 1.166666667 = 2.70325741 t = 2.70325741 Simplifying t = 2.70325741

Subproblem 2

t + -1.166666667 = -1.536590743 Simplifying t + -1.166666667 = -1.536590743 Reorder the terms: -1.166666667 + t = -1.536590743 Solving -1.166666667 + t = -1.536590743 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + t = -1.536590743 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + t = -1.536590743 + 1.166666667 t = -1.536590743 + 1.166666667 Combine like terms: -1.536590743 + 1.166666667 = -0.369924076 t = -0.369924076 Simplifying t = -0.369924076

Solution

The solution to the problem is based on the solutions from the subproblems. t = {2.70325741, -0.369924076}

See similar equations:

| 2b-1=3b | | 3*1.6+12=5*1.6+4+3*1.6 | | 8w-2w+5=4-3+5w | | 1x/3=-7 | | -19=D-6 | | 5/6=15/t | | 18+9x=22 | | 6(11+s)=93 | | 23-x=-23 | | 1728x4/3 | | 7=(5=a)/4 | | 6(x+9)=5x | | log[2](x^2-6)=log[2](3x+4) | | 35/8x19/9= | | 56w^2+31w+3= | | 3sin(x+10)=2cos(x-10) | | -116=-3x+4(-x-8) | | 9w-6=-2w+12 | | 46+5=1+5b | | -5(3-9k)=-27 | | x*x+50=300 | | log[4](5x-4)=log[4](3x+8) | | 72.48x+6=18.08x+0 | | 7=8x+8 | | x^2+6x+126=0 | | e-2w+5=4-3+5e | | 6.2=log(I) | | 72.48x+6=18.08 | | 17+x=-4 | | y=0.8x-3.8 | | -8(4d-7)=-24 | | q=10-2t |

Equations solver categories