6x(3x-9)=90

Simple and best practice solution for 6x(3x-9)=90 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 6x(3x-9)=90 equation: 


Simplifying
6x(3x + -9) = 90

Reorder the terms:
6x(-9 + 3x) = 90
(-9 * 6x + 3x * 6x) = 90
(-54x + 18x2) = 90

Solving
-54x + 18x2 = 90

Solving for variable 'x'.

Reorder the terms:
-90 + -54x + 18x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-90 + -54x + 18x2 = 0

Factor out the Greatest Common Factor (GCF), '18'.
18(-5 + -3x + x2) = 0

Ignore the factor 18.

Subproblem 1
Set the factor '(-5 + -3x + x2)' equal to zero and attempt to solve:

Simplifying
-5 + -3x + x2 = 0

Solving
-5 + -3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -3x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + -3x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3x + x2 = 0 + 5
-3x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
-3x + x2 = 5

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 = 5 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 5 + 2.25

Combine like terms: 5 + 2.25 = 7.25
2.25 + -3x + x2 = 7.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 7.25

Calculate the square root of the right side: 2.692582404

Break this problem into two subproblems by setting 
(x + -1.5) equal to 2.692582404 and -2.692582404.


Subproblem 1
x + -1.5 = 2.692582404

Simplifying
x + -1.5 = 2.692582404

Reorder the terms:
-1.5 + x = 2.692582404

Solving
-1.5 + x = 2.692582404

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 = 2.692582404 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 2.692582404 + 1.5
x = 2.692582404 + 1.5

Combine like terms: 2.692582404 + 1.5 = 4.192582404
x = 4.192582404

Simplifying
x = 4.192582404


Subproblem 2
x + -1.5 = -2.692582404

Simplifying
x + -1.5 = -2.692582404

Reorder the terms:
-1.5 + x = -2.692582404

Solving
-1.5 + x = -2.692582404

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 = -2.692582404 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -2.692582404 + 1.5
x = -2.692582404 + 1.5

Combine like terms: -2.692582404 + 1.5 = -1.192582404
x = -1.192582404

Simplifying
x = -1.192582404


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.192582404, -1.192582404}
Solution
x = {4.192582404, -1.192582404}

See similar equations:

| -6a-15=-a-7-6a | | 7+6x=8x-5 | | 11m+6=83 | | 3(5x-3)-4(2x+1)=5x-2 | | 7k-11=7k-4 | | 9x+18=11x-32 | | 12b-72=84 | | -81+x=105+7x | | -11x=7 | | 5(k+5)-2(n-3)=62 | | 19x=3y | | 2(3-4x)-5(2x+3)=x-17 | | 4(1-2x)-3(3-y)=-12 | | 14=8x-9 | | 2(3x-1)-(y+4)=-7 | | 2(3x-1)-(y+4)=-12 | | 3x-2+6=4+7x-4x | | 7-4n=13 | | -32-3/5f=-17 | | 4x-1=2(2x+3) | | h=-38x+77813 | | 96-5g=51 | | 7x+8=6x+1 | | 7h-27=36 | | 0.10x+0.25(11-x)=1.70 | | 25x+10(11-x)=1.70 | | x+(11-x)=1.70 | | 26=14-2m | | 5=9-2x | | 6y+9-4y=-3 | | 4(w+0.3)=66.48 | | -2(t-9)-(t+2)=1 |

Equations solver categories