(5t-4)(t+11)=(2t-9)(t+1)

Simple and best practice solution for (5t-4)(t+11)=(2t-9)(t+1) 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 (5t-4)(t+11)=(2t-9)(t+1) equation: 


Simplifying
(5t + -4)(t + 11) = (2t + -9)(t + 1)

Reorder the terms:
(-4 + 5t)(t + 11) = (2t + -9)(t + 1)

Reorder the terms:
(-4 + 5t)(11 + t) = (2t + -9)(t + 1)

Multiply (-4 + 5t) * (11 + t)
(-4(11 + t) + 5t * (11 + t)) = (2t + -9)(t + 1)
((11 * -4 + t * -4) + 5t * (11 + t)) = (2t + -9)(t + 1)
((-44 + -4t) + 5t * (11 + t)) = (2t + -9)(t + 1)
(-44 + -4t + (11 * 5t + t * 5t)) = (2t + -9)(t + 1)
(-44 + -4t + (55t + 5t2)) = (2t + -9)(t + 1)

Combine like terms: -4t + 55t = 51t
(-44 + 51t + 5t2) = (2t + -9)(t + 1)

Reorder the terms:
-44 + 51t + 5t2 = (-9 + 2t)(t + 1)

Reorder the terms:
-44 + 51t + 5t2 = (-9 + 2t)(1 + t)

Multiply (-9 + 2t) * (1 + t)
-44 + 51t + 5t2 = (-9(1 + t) + 2t * (1 + t))
-44 + 51t + 5t2 = ((1 * -9 + t * -9) + 2t * (1 + t))
-44 + 51t + 5t2 = ((-9 + -9t) + 2t * (1 + t))
-44 + 51t + 5t2 = (-9 + -9t + (1 * 2t + t * 2t))
-44 + 51t + 5t2 = (-9 + -9t + (2t + 2t2))

Combine like terms: -9t + 2t = -7t
-44 + 51t + 5t2 = (-9 + -7t + 2t2)

Solving
-44 + 51t + 5t2 = -9 + -7t + 2t2

Solving for variable 't'.

Reorder the terms:
-44 + 9 + 51t + 7t + 5t2 + -2t2 = -9 + -7t + 2t2 + 9 + 7t + -2t2

Combine like terms: -44 + 9 = -35
-35 + 51t + 7t + 5t2 + -2t2 = -9 + -7t + 2t2 + 9 + 7t + -2t2

Combine like terms: 51t + 7t = 58t
-35 + 58t + 5t2 + -2t2 = -9 + -7t + 2t2 + 9 + 7t + -2t2

Combine like terms: 5t2 + -2t2 = 3t2
-35 + 58t + 3t2 = -9 + -7t + 2t2 + 9 + 7t + -2t2

Reorder the terms:
-35 + 58t + 3t2 = -9 + 9 + -7t + 7t + 2t2 + -2t2

Combine like terms: -9 + 9 = 0
-35 + 58t + 3t2 = 0 + -7t + 7t + 2t2 + -2t2
-35 + 58t + 3t2 = -7t + 7t + 2t2 + -2t2

Combine like terms: -7t + 7t = 0
-35 + 58t + 3t2 = 0 + 2t2 + -2t2
-35 + 58t + 3t2 = 2t2 + -2t2

Combine like terms: 2t2 + -2t2 = 0
-35 + 58t + 3t2 = 0

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

Divide each side by '3'.
-11.66666667 + 19.33333333t + t2 = 0

Move the constant term to the right:

Add '11.66666667' to each side of the equation.
-11.66666667 + 19.33333333t + 11.66666667 + t2 = 0 + 11.66666667

Reorder the terms:
-11.66666667 + 11.66666667 + 19.33333333t + t2 = 0 + 11.66666667

Combine like terms: -11.66666667 + 11.66666667 = 0.00000000
0.00000000 + 19.33333333t + t2 = 0 + 11.66666667
19.33333333t + t2 = 0 + 11.66666667

Combine like terms: 0 + 11.66666667 = 11.66666667
19.33333333t + t2 = 11.66666667

The t term is 19.33333333t.  Take half its coefficient (9.666666665).
Square it (93.44444441) and add it to both sides.

Add '93.44444441' to each side of the equation.
19.33333333t + 93.44444441 + t2 = 11.66666667 + 93.44444441

Reorder the terms:
93.44444441 + 19.33333333t + t2 = 11.66666667 + 93.44444441

Combine like terms: 11.66666667 + 93.44444441 = 105.11111108
93.44444441 + 19.33333333t + t2 = 105.11111108

Factor a perfect square on the left side:
(t + 9.666666665)(t + 9.666666665) = 105.11111108

Calculate the square root of the right side: 10.252370998

Break this problem into two subproblems by setting 
(t + 9.666666665) equal to 10.252370998 and -10.252370998.


Subproblem 1
t + 9.666666665 = 10.252370998

Simplifying
t + 9.666666665 = 10.252370998

Reorder the terms:
9.666666665 + t = 10.252370998

Solving
9.666666665 + t = 10.252370998

Solving for variable 't'.

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

Add '-9.666666665' to each side of the equation.
9.666666665 + -9.666666665 + t = 10.252370998 + -9.666666665

Combine like terms: 9.666666665 + -9.666666665 = 0.000000000
0.000000000 + t = 10.252370998 + -9.666666665
t = 10.252370998 + -9.666666665

Combine like terms: 10.252370998 + -9.666666665 = 0.585704333
t = 0.585704333

Simplifying
t = 0.585704333


Subproblem 2
t + 9.666666665 = -10.252370998

Simplifying
t + 9.666666665 = -10.252370998

Reorder the terms:
9.666666665 + t = -10.252370998

Solving
9.666666665 + t = -10.252370998

Solving for variable 't'.

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

Add '-9.666666665' to each side of the equation.
9.666666665 + -9.666666665 + t = -10.252370998 + -9.666666665

Combine like terms: 9.666666665 + -9.666666665 = 0.000000000
0.000000000 + t = -10.252370998 + -9.666666665
t = -10.252370998 + -9.666666665

Combine like terms: -10.252370998 + -9.666666665 = -19.919037663
t = -19.919037663

Simplifying
t = -19.919037663


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.585704333, -19.919037663}

See similar equations:

| 8t-2t=3 | | 3.5*12=X*310*Y | | 2x^2-14=-3 | | 8y-35=-24x | | x=-2x^2+6x+10 | | 3.14x3(3+9x2+rx2) | | 4x-4y=6 | | y=1.6x+4 | | x-3(5)=-18 | | y=5/3x+4 | | 9+11x= | | y^2-3y-9=0 | | 4*(k+2)-8k-5=3k+9-2*(k+6) | | -16t^2+45t+2.5=5.5 | | 3x3 | | (3m+4)m-3m+5 | | 5+4x=19-4x | | (4x+12)(5x-15)(7x+21)=0 | | a-(1/2)a=3 | | 52-x+y= | | (5x+1)(5x-1)=0 | | t+2t^2/t=43 | | 9+7-2y= | | t+2t^2=43 | | (7x-1)(1-7x)=0 | | 6y-4x= | | 5(x-2)=2 | | 5x(9x-9)=0 | | 9y^2=100 | | 12y-3x+5.6= | | 6x^2+12x+13=2x^2+4 | | 9(x-7)=7 |

Equations solver categories