9x(x-3)=6(x+4)

Simple and best practice solution for 9x(x-3)=6(x+4) 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 9x(x-3)=6(x+4) equation: 


Simplifying
9x(x + -3) = 6(x + 4)

Reorder the terms:
9x(-3 + x) = 6(x + 4)
(-3 * 9x + x * 9x) = 6(x + 4)
(-27x + 9x2) = 6(x + 4)

Reorder the terms:
-27x + 9x2 = 6(4 + x)
-27x + 9x2 = (4 * 6 + x * 6)
-27x + 9x2 = (24 + 6x)

Solving
-27x + 9x2 = 24 + 6x

Solving for variable 'x'.

Reorder the terms:
-24 + -27x + -6x + 9x2 = 24 + 6x + -24 + -6x

Combine like terms: -27x + -6x = -33x
-24 + -33x + 9x2 = 24 + 6x + -24 + -6x

Reorder the terms:
-24 + -33x + 9x2 = 24 + -24 + 6x + -6x

Combine like terms: 24 + -24 = 0
-24 + -33x + 9x2 = 0 + 6x + -6x
-24 + -33x + 9x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-24 + -33x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-8 + -11x + 3x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-8 + -11x + 3x2)' equal to zero and attempt to solve:

Simplifying
-8 + -11x + 3x2 = 0

Solving
-8 + -11x + 3x2 = 0

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

Divide each side by '3'.
-2.666666667 + -3.666666667x + x2 = 0

Move the constant term to the right:

Add '2.666666667' to each side of the equation.
-2.666666667 + -3.666666667x + 2.666666667 + x2 = 0 + 2.666666667

Reorder the terms:
-2.666666667 + 2.666666667 + -3.666666667x + x2 = 0 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + -3.666666667x + x2 = 0 + 2.666666667
-3.666666667x + x2 = 0 + 2.666666667

Combine like terms: 0 + 2.666666667 = 2.666666667
-3.666666667x + x2 = 2.666666667

The x term is -3.666666667x.  Take half its coefficient (-1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
-3.666666667x + 3.361111114 + x2 = 2.666666667 + 3.361111114

Reorder the terms:
3.361111114 + -3.666666667x + x2 = 2.666666667 + 3.361111114

Combine like terms: 2.666666667 + 3.361111114 = 6.027777781
3.361111114 + -3.666666667x + x2 = 6.027777781

Factor a perfect square on the left side:
(x + -1.833333334)(x + -1.833333334) = 6.027777781

Calculate the square root of the right side: 2.455153311

Break this problem into two subproblems by setting 
(x + -1.833333334) equal to 2.455153311 and -2.455153311.


Subproblem 1
x + -1.833333334 = 2.455153311

Simplifying
x + -1.833333334 = 2.455153311

Reorder the terms:
-1.833333334 + x = 2.455153311

Solving
-1.833333334 + x = 2.455153311

Solving for variable 'x'.

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

Add '1.833333334' to each side of the equation.
-1.833333334 + 1.833333334 + x = 2.455153311 + 1.833333334

Combine like terms: -1.833333334 + 1.833333334 = 0.000000000
0.000000000 + x = 2.455153311 + 1.833333334
x = 2.455153311 + 1.833333334

Combine like terms: 2.455153311 + 1.833333334 = 4.288486645
x = 4.288486645

Simplifying
x = 4.288486645


Subproblem 2
x + -1.833333334 = -2.455153311

Simplifying
x + -1.833333334 = -2.455153311

Reorder the terms:
-1.833333334 + x = -2.455153311

Solving
-1.833333334 + x = -2.455153311

Solving for variable 'x'.

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

Add '1.833333334' to each side of the equation.
-1.833333334 + 1.833333334 + x = -2.455153311 + 1.833333334

Combine like terms: -1.833333334 + 1.833333334 = 0.000000000
0.000000000 + x = -2.455153311 + 1.833333334
x = -2.455153311 + 1.833333334

Combine like terms: -2.455153311 + 1.833333334 = -0.621819977
x = -0.621819977

Simplifying
x = -0.621819977


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.288486645, -0.621819977}
Solution
x = {4.288486645, -0.621819977}

See similar equations:

| 5v^2-17v+6=0 | | 2x^2-16+4=0 | | x^2+6=83 | | X/4-12=3 | | 21+134+5x=180 | | 5(x-3)=0.5 | | (3x+7)x(3x+7)= | | 12v^2=24+28v | | 3(x+1)=2(1-x) | | 0.91+0.05*x+0.01*x^13=x | | 12t-5=7t | | .7x+.32(7)=.5(21) | | -4w+16-4w=-22 | | 3z/7-4=10 | | 4(4x-6)=-20 | | 5(2x-3)=-75 | | 3sinx=-3sinx-4 | | 10y=5x-3 | | 2n^2+24=19n | | 8(a+1)=55.2 | | 4x^2-25y^2-32x+164=0 | | 25p^2-1=0 | | .5x^3-12.5x=0 | | 4x+8=129 | | 4z-7=2 | | 5x^2=5-2x | | x-7-2=-7 | | (4x+1)-(x-2)=9 | | 4x-9=-39-8x | | 3tanx+3=15 | | Z-9-6=8 | | 8e-7=20.2 |

Equations solver categories