3x(2x-3)=2x+9

Simple and best practice solution for 3x(2x-3)=2x+9 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 3x(2x-3)=2x+9 equation:


Simplifying
3x(2x + -3) = 2x + 9

Reorder the terms:
3x(-3 + 2x) = 2x + 9
(-3 * 3x + 2x * 3x) = 2x + 9
(-9x + 6x2) = 2x + 9

Reorder the terms:
-9x + 6x2 = 9 + 2x

Solving
-9x + 6x2 = 9 + 2x

Solving for variable 'x'.

Reorder the terms:
-9 + -9x + -2x + 6x2 = 9 + 2x + -9 + -2x

Combine like terms: -9x + -2x = -11x
-9 + -11x + 6x2 = 9 + 2x + -9 + -2x

Reorder the terms:
-9 + -11x + 6x2 = 9 + -9 + 2x + -2x

Combine like terms: 9 + -9 = 0
-9 + -11x + 6x2 = 0 + 2x + -2x
-9 + -11x + 6x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-9 + -11x + 6x2 = 0

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

Divide each side by '6'.
-1.5 + -1.833333333x + x2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + -1.833333333x + 1.5 + x2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + -1.833333333x + x2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + -1.833333333x + x2 = 0 + 1.5
-1.833333333x + x2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
-1.833333333x + x2 = 1.5

The x term is -1.833333333x.  Take half its coefficient (-0.9166666665).
Square it (0.8402777775) and add it to both sides.

Add '0.8402777775' to each side of the equation.
-1.833333333x + 0.8402777775 + x2 = 1.5 + 0.8402777775

Reorder the terms:
0.8402777775 + -1.833333333x + x2 = 1.5 + 0.8402777775

Combine like terms: 1.5 + 0.8402777775 = 2.3402777775
0.8402777775 + -1.833333333x + x2 = 2.3402777775

Factor a perfect square on the left side:
(x + -0.9166666665)(x + -0.9166666665) = 2.3402777775

Calculate the square root of the right side: 1.529796646

Break this problem into two subproblems by setting 
(x + -0.9166666665) equal to 1.529796646 and -1.529796646.

Subproblem 1

x + -0.9166666665 = 1.529796646 Simplifying x + -0.9166666665 = 1.529796646 Reorder the terms: -0.9166666665 + x = 1.529796646 Solving -0.9166666665 + x = 1.529796646 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9166666665' to each side of the equation. -0.9166666665 + 0.9166666665 + x = 1.529796646 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + x = 1.529796646 + 0.9166666665 x = 1.529796646 + 0.9166666665 Combine like terms: 1.529796646 + 0.9166666665 = 2.4464633125 x = 2.4464633125 Simplifying x = 2.4464633125

Subproblem 2

x + -0.9166666665 = -1.529796646 Simplifying x + -0.9166666665 = -1.529796646 Reorder the terms: -0.9166666665 + x = -1.529796646 Solving -0.9166666665 + x = -1.529796646 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9166666665' to each side of the equation. -0.9166666665 + 0.9166666665 + x = -1.529796646 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + x = -1.529796646 + 0.9166666665 x = -1.529796646 + 0.9166666665 Combine like terms: -1.529796646 + 0.9166666665 = -0.6131299795 x = -0.6131299795 Simplifying x = -0.6131299795

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.4464633125, -0.6131299795}

See similar equations:

| 82a^2-38a=279 | | 5x-2(4x-1)=12x-1 | | 3(x-1)+2(x+1)=-14 | | 3x-3=(2/5)(5x+10) | | 36-5x=4x+23 | | (91a^2-9a-10)-(173a^2-47a+8)=297 | | 14-7x=68-21x | | 2(0)-6y=12 | | 22=x+5+x+1 | | 4x-3x=8 | | (7y^6/2y^7)/(35y/4y^4) | | f(x)=2x^2-15*x+18 | | y^2-1/4=6 | | f(x)=x^3+3*x^2-4*x-12 | | y=2x-15y | | 2z+3=11 | | 0.3x-5.4=2.7+0.8x | | 5a-7/(5a/a-5)/10a | | 3n+4=3.1 | | 5y-35=2x-8 | | 2.5x+1.3=1.4x+1.3 | | 3(2-4a)=18 | | 6.8+0.4x=1.6 | | 10x-36=13x+9 | | x-0.35=-0.1 | | -5f-3=7 | | 9w-4w-4=21 | | 10x+7x-2x=2(7x+5) | | -12x+3=-21 | | y-68=34 | | 21=11x-12 | | m-8=-11 |

Equations solver categories