3(x^2-3x-6)=0

Simple and best practice solution for 3(x^2-3x-6)=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 3(x^2-3x-6)=0 equation: 


Simplifying
3(x2 + -3x + -6) = 0

Reorder the terms:
3(-6 + -3x + x2) = 0
(-6 * 3 + -3x * 3 + x2 * 3) = 0
(-18 + -9x + 3x2) = 0

Solving
-18 + -9x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-6 + -3x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-6 + -3x + x2)' equal to zero and attempt to solve:

Simplifying
-6 + -3x + x2 = 0

Solving
-6 + -3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -3x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + -3x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -3x + x2 = 0 + 6
-3x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
-3x + x2 = 6

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 6 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 6 + 2.25

Combine like terms: 6 + 2.25 = 8.25
2.25 + -3x + x2 = 8.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(x + -1.5) equal to 2.872281323 and -2.872281323.


Subproblem 1
x + -1.5 = 2.872281323

Simplifying
x + -1.5 = 2.872281323

Reorder the terms:
-1.5 + x = 2.872281323

Solving
-1.5 + x = 2.872281323

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 2.872281323 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 2.872281323 + 1.5
x = 2.872281323 + 1.5

Combine like terms: 2.872281323 + 1.5 = 4.372281323
x = 4.372281323

Simplifying
x = 4.372281323


Subproblem 2
x + -1.5 = -2.872281323

Simplifying
x + -1.5 = -2.872281323

Reorder the terms:
-1.5 + x = -2.872281323

Solving
-1.5 + x = -2.872281323

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -2.872281323 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -2.872281323 + 1.5
x = -2.872281323 + 1.5

Combine like terms: -2.872281323 + 1.5 = -1.372281323
x = -1.372281323

Simplifying
x = -1.372281323


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.372281323, -1.372281323}
Solution
x = {4.372281323, -1.372281323}

See similar equations:

| 2(7)-2y=14 | | (-4)+s=(-4) | | 12n+4n-11n=10 | | 2x^2+28+96=0 | | 1-w=6 | | 3*-.75-1=7*-.75+2 | | m+(-8.5)=(-0.6) | | -8-4p=24 | | (-6)=(-6)+g | | c^2+9c-18= | | (5pq)(12pq)= | | x^2+3y^2-13=0 | | 4(5-2m)=-6(3m+8)+13 | | t+1=(-4) | | 2x-2(7)=14 | | 4.9T^2+2T+1.2=0 | | 4=5x-4x | | 12+(-4)x=48 | | 12=4x-2+6 | | 6(5-2a)=-4(3a+2) | | 75-6x=4x-3p | | 14=-5a-1 | | 150+6m=96+15m | | 5x-9=10x+15 | | -2x-8y=26 | | 2y+6+4y-2= | | 3x+7y-8=0 | | y+-1(-7)=-2(x-4) | | 5k-3=82 | | 8x-75=x | | 0.4w+2.45=8.75 | | -5(x)-8=-33 |

Equations solver categories