3x(2x-3)=x+1

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


Simplifying
3x(2x + -3) = x + 1

Reorder the terms:
3x(-3 + 2x) = x + 1
(-3 * 3x + 2x * 3x) = x + 1
(-9x + 6x2) = x + 1

Reorder the terms:
-9x + 6x2 = 1 + x

Solving
-9x + 6x2 = 1 + x

Solving for variable 'x'.

Reorder the terms:
-1 + -9x + -1x + 6x2 = 1 + x + -1 + -1x

Combine like terms: -9x + -1x = -10x
-1 + -10x + 6x2 = 1 + x + -1 + -1x

Reorder the terms:
-1 + -10x + 6x2 = 1 + -1 + x + -1x

Combine like terms: 1 + -1 = 0
-1 + -10x + 6x2 = 0 + x + -1x
-1 + -10x + 6x2 = x + -1x

Combine like terms: x + -1x = 0
-1 + -10x + 6x2 = 0

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

Divide each side by '6'.
-0.1666666667 + -1.666666667x + x2 = 0

Move the constant term to the right:

Add '0.1666666667' to each side of the equation.
-0.1666666667 + -1.666666667x + 0.1666666667 + x2 = 0 + 0.1666666667

Reorder the terms:
-0.1666666667 + 0.1666666667 + -1.666666667x + x2 = 0 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + -1.666666667x + x2 = 0 + 0.1666666667
-1.666666667x + x2 = 0 + 0.1666666667

Combine like terms: 0 + 0.1666666667 = 0.1666666667
-1.666666667x + x2 = 0.1666666667

The x term is -1.666666667x.  Take half its coefficient (-0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
-1.666666667x + 0.6944444447 + x2 = 0.1666666667 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667x + x2 = 0.1666666667 + 0.6944444447

Combine like terms: 0.1666666667 + 0.6944444447 = 0.8611111114
0.6944444447 + -1.666666667x + x2 = 0.8611111114

Factor a perfect square on the left side:
(x + -0.8333333335)(x + -0.8333333335) = 0.8611111114

Calculate the square root of the right side: 0.927960727

Break this problem into two subproblems by setting 
(x + -0.8333333335) equal to 0.927960727 and -0.927960727.

Subproblem 1

x + -0.8333333335 = 0.927960727 Simplifying x + -0.8333333335 = 0.927960727 Reorder the terms: -0.8333333335 + x = 0.927960727 Solving -0.8333333335 + x = 0.927960727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = 0.927960727 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 0.927960727 + 0.8333333335 x = 0.927960727 + 0.8333333335 Combine like terms: 0.927960727 + 0.8333333335 = 1.7612940605 x = 1.7612940605 Simplifying x = 1.7612940605

Subproblem 2

x + -0.8333333335 = -0.927960727 Simplifying x + -0.8333333335 = -0.927960727 Reorder the terms: -0.8333333335 + x = -0.927960727 Solving -0.8333333335 + x = -0.927960727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = -0.927960727 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -0.927960727 + 0.8333333335 x = -0.927960727 + 0.8333333335 Combine like terms: -0.927960727 + 0.8333333335 = -0.0946273935 x = -0.0946273935 Simplifying x = -0.0946273935

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.7612940605, -0.0946273935}

See similar equations:

| (3z-2)(5-z)=0 | | -6(x+1)-2x=-11-7x | | 19p+14q+p-3q-7p= | | 5x-13=22 | | 3(x+5)=4(x-2) | | -9(4b-3)+(37b-5)=0 | | -14-4x=2x+23 | | 13m+4n-5m+8n= | | x^4+4x^3-3x^2+8x-10=0 | | -16(z+1)+5(4z-5)=3(z-4)+11 | | 10x-8=4x+46 | | 4x-21=6x+5 | | 2(9-4)=4a-(2a+4) | | 2+5(8-2p)=22-6p | | x=50x+25 | | 4x(2+3)=0 | | 7s-1=t | | -4v(v-3)(v-1)=0 | | 5x+7y=19 | | -10p-2(p+2)=-11(1+p) | | (z+4)(z-8)=0 | | t=-2s-1 | | 4x-15=49 | | 0=t^2+5t+36 | | -7x+2(2x-8)=2 | | 7x-8y+5x+8y-x= | | x^4+10x^2=6x^3 | | -7(6-4x)-x=-13-2x | | (36)+8y+4+(36)=4y+8 | | Xy+x-xy-x+y= | | 3z=12-18 | | 2+6(2-8m)=-27-7m |

Equations solver categories