6x(2x+3)=1

Simple and best practice solution for 6x(2x+3)=1 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(2x+3)=1 equation:


Simplifying
6x(2x + 3) = 1

Reorder the terms:
6x(3 + 2x) = 1
(3 * 6x + 2x * 6x) = 1
(18x + 12x2) = 1

Solving
18x + 12x2 = 1

Solving for variable 'x'.

Reorder the terms:
-1 + 18x + 12x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 18x + 12x2 = 0

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

Divide each side by '12'.
-0.08333333333 + 1.5x + x2 = 0

Move the constant term to the right:

Add '0.08333333333' to each side of the equation.
-0.08333333333 + 1.5x + 0.08333333333 + x2 = 0 + 0.08333333333

Reorder the terms:
-0.08333333333 + 0.08333333333 + 1.5x + x2 = 0 + 0.08333333333

Combine like terms: -0.08333333333 + 0.08333333333 = 0.00000000000
0.00000000000 + 1.5x + x2 = 0 + 0.08333333333
1.5x + x2 = 0 + 0.08333333333

Combine like terms: 0 + 0.08333333333 = 0.08333333333
1.5x + x2 = 0.08333333333

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 0.08333333333 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 0.08333333333 + 0.5625

Combine like terms: 0.08333333333 + 0.5625 = 0.64583333333
0.5625 + 1.5x + x2 = 0.64583333333

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 0.64583333333

Calculate the square root of the right side: 0.803637563

Break this problem into two subproblems by setting 
(x + 0.75) equal to 0.803637563 and -0.803637563.

Subproblem 1

x + 0.75 = 0.803637563 Simplifying x + 0.75 = 0.803637563 Reorder the terms: 0.75 + x = 0.803637563 Solving 0.75 + x = 0.803637563 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 0.803637563 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 0.803637563 + -0.75 x = 0.803637563 + -0.75 Combine like terms: 0.803637563 + -0.75 = 0.053637563 x = 0.053637563 Simplifying x = 0.053637563

Subproblem 2

x + 0.75 = -0.803637563 Simplifying x + 0.75 = -0.803637563 Reorder the terms: 0.75 + x = -0.803637563 Solving 0.75 + x = -0.803637563 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -0.803637563 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -0.803637563 + -0.75 x = -0.803637563 + -0.75 Combine like terms: -0.803637563 + -0.75 = -1.553637563 x = -1.553637563 Simplifying x = -1.553637563

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.053637563, -1.553637563}

See similar equations:

| -6.5x+28=2-1.3y | | -2(3y-4)=-6y+8 | | -12g=1 | | -7=9f+20 | | (3x+20)=(5x-8) | | 9k-3=-11 | | 7m-9=5 | | 5X^2-X+14=0 | | 4+5n=29 | | (x+20)+3x=60 | | 18=3G+6 | | -2g+-16=4 | | 2(6+5)-1=25 | | x=8y | | 5+2p=45 | | 5x^3+6x^2+6x+1=0 | | 2x+7=x+8 | | 4(2y-4)=5y-9 | | 7-8(3k+5)= | | 3d+81=117 | | 17-(8-n)=17 | | 17-(8-n)=18 | | 3.5(c+8)+c=12.5 | | 4m+6=70 | | 3.5(c+8)+c=12 | | 98.70=32.9g | | c=32.9g | | -5+x=6x | | 5x+30=24x-12 | | 3.5z=7 | | 3-x=x | | 10-3b^2=-11 |

Equations solver categories