2(x+1)=3(x-4)x

Simple and best practice solution for 2(x+1)=3(x-4)x 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 2(x+1)=3(x-4)x equation:


Simplifying
2(x + 1) = 3(x + -4) * x

Reorder the terms:
2(1 + x) = 3(x + -4) * x
(1 * 2 + x * 2) = 3(x + -4) * x
(2 + 2x) = 3(x + -4) * x

Reorder the terms:
2 + 2x = 3(-4 + x) * x

Reorder the terms for easier multiplication:
2 + 2x = 3x(-4 + x)
2 + 2x = (-4 * 3x + x * 3x)
2 + 2x = (-12x + 3x2)

Solving
2 + 2x = -12x + 3x2

Solving for variable 'x'.

Combine like terms: 2x + 12x = 14x
2 + 14x + -3x2 = -12x + 3x2 + 12x + -3x2

Reorder the terms:
2 + 14x + -3x2 = -12x + 12x + 3x2 + -3x2

Combine like terms: -12x + 12x = 0
2 + 14x + -3x2 = 0 + 3x2 + -3x2
2 + 14x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
2 + 14x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-0.6666666667 + -4.666666667x + x2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + -4.666666667x + 0.6666666667 + x2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + -4.666666667x + x2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + -4.666666667x + x2 = 0 + 0.6666666667
-4.666666667x + x2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
-4.666666667x + x2 = 0.6666666667

The x term is -4.666666667x.  Take half its coefficient (-2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
-4.666666667x + 5.444444448 + x2 = 0.6666666667 + 5.444444448

Reorder the terms:
5.444444448 + -4.666666667x + x2 = 0.6666666667 + 5.444444448

Combine like terms: 0.6666666667 + 5.444444448 = 6.1111111147
5.444444448 + -4.666666667x + x2 = 6.1111111147

Factor a perfect square on the left side:
(x + -2.333333334)(x + -2.333333334) = 6.1111111147

Calculate the square root of the right side: 2.472066163

Break this problem into two subproblems by setting 
(x + -2.333333334) equal to 2.472066163 and -2.472066163.

Subproblem 1

x + -2.333333334 = 2.472066163 Simplifying x + -2.333333334 = 2.472066163 Reorder the terms: -2.333333334 + x = 2.472066163 Solving -2.333333334 + x = 2.472066163 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + x = 2.472066163 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x = 2.472066163 + 2.333333334 x = 2.472066163 + 2.333333334 Combine like terms: 2.472066163 + 2.333333334 = 4.805399497 x = 4.805399497 Simplifying x = 4.805399497

Subproblem 2

x + -2.333333334 = -2.472066163 Simplifying x + -2.333333334 = -2.472066163 Reorder the terms: -2.333333334 + x = -2.472066163 Solving -2.333333334 + x = -2.472066163 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + x = -2.472066163 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x = -2.472066163 + 2.333333334 x = -2.472066163 + 2.333333334 Combine like terms: -2.472066163 + 2.333333334 = -0.138732829 x = -0.138732829 Simplifying x = -0.138732829

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.805399497, -0.138732829}

See similar equations:

| 2(10k-2)=2(9k-5) | | 16-8y=-24x | | 8m=15m-3m-20 | | 6(n-7)-(3-4n)=9n | | 2x-19=25+7x | | 12p+17q+p-6q-4p= | | -6r+4r=-30 | | 1+9a-8=a | | x^2+12x+13=4 | | a/4-6=20 | | 6(y+3)+1= | | 75+4x-9=180 | | 48p^2-306p+108=0 | | 3(5x+1)=9(x-3) | | 22=-2k+3+7 | | ab+5x+y=x-a(b+c) | | -8=2+7n+4 | | 6a+4a=180 | | 9x+6=4x+7 | | x-5=5x-1 | | z+8=15 | | 6(x-1)-4=4-(x+1) | | -(3k-2)=2(k+2) | | x-=5x-1 | | 10x^2-29x-72=0 | | 4d+1=3d+8 | | 2x+0.5x-2=-0.25x+2-0.25x | | 9x+3=12x+9 | | h^2+4=8h-3 | | p-14=-11 | | -5x(x-3)=15 | | 36=5c-7 |

Equations solver categories