2x(6x+18)=90

Simple and best practice solution for 2x(6x+18)=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 2x(6x+18)=90 equation: 


Simplifying
2x(6x + 18) = 90

Reorder the terms:
2x(18 + 6x) = 90
(18 * 2x + 6x * 2x) = 90
(36x + 12x2) = 90

Solving
36x + 12x2 = 90

Solving for variable 'x'.

Reorder the terms:
-90 + 36x + 12x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-90 + 36x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-15 + 6x + 2x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-15 + 6x + 2x2)' equal to zero and attempt to solve:

Simplifying
-15 + 6x + 2x2 = 0

Solving
-15 + 6x + 2x2 = 0

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

Divide each side by '2'.
-7.5 + 3x + x2 = 0

Move the constant term to the right:

Add '7.5' to each side of the equation.
-7.5 + 3x + 7.5 + x2 = 0 + 7.5

Reorder the terms:
-7.5 + 7.5 + 3x + x2 = 0 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + 3x + x2 = 0 + 7.5
3x + x2 = 0 + 7.5

Combine like terms: 0 + 7.5 = 7.5
3x + x2 = 7.5

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 = 7.5 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 7.5 + 2.25

Combine like terms: 7.5 + 2.25 = 9.75
2.25 + 3x + x2 = 9.75

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 9.75

Calculate the square root of the right side: 3.122498999

Break this problem into two subproblems by setting 
(x + 1.5) equal to 3.122498999 and -3.122498999.


Subproblem 1
x + 1.5 = 3.122498999

Simplifying
x + 1.5 = 3.122498999

Reorder the terms:
1.5 + x = 3.122498999

Solving
1.5 + x = 3.122498999

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 = 3.122498999 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 3.122498999 + -1.5
x = 3.122498999 + -1.5

Combine like terms: 3.122498999 + -1.5 = 1.622498999
x = 1.622498999

Simplifying
x = 1.622498999


Subproblem 2
x + 1.5 = -3.122498999

Simplifying
x + 1.5 = -3.122498999

Reorder the terms:
1.5 + x = -3.122498999

Solving
1.5 + x = -3.122498999

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 = -3.122498999 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -3.122498999 + -1.5
x = -3.122498999 + -1.5

Combine like terms: -3.122498999 + -1.5 = -4.622498999
x = -4.622498999

Simplifying
x = -4.622498999


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.622498999, -4.622498999}
Solution
x = {1.622498999, -4.622498999}

See similar equations:

| G/8-2=1 | | n+4.26=17.4 | | 3x-7=5+2(x-8) | | 8v^2-20=0 | | 22/7÷7/3 | | 5y+7=77 | | 20x-16=164 | | X*8x=96 | | X+16=-2x-3 | | 9(x-7)=5(x-3) | | X*8x= | | Z/4-5=1 | | (P+q)2= | | 6p+4r-5p+2r= | | 24=n/6 | | F/5-3=2 | | -1+2(2x-3)=-5x-16 | | 9(x-7)+5=2x-9 | | 22=(10x)+4 | | 16-3t=4 | | 4(c-d)= | | 10q+8q-136=68-8q | | G/4-1=3 | | 3x^3-243x=0 | | 4(x-7)+5=2x-9 | | (cotx)(sinx)= | | 8x+7=37+3x | | 3yx+3yx= | | 10q+8q-136=34-8q | | 12-12x=3x^2 | | 18v-18v= | | -204=-12v |

Equations solver categories