(6x-7)(9x-8)=180

Simple and best practice solution for (6x-7)(9x-8)=180 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-7)(9x-8)=180 equation:


Simplifying
(6x + -7)(9x + -8) = 180

Reorder the terms:
(-7 + 6x)(9x + -8) = 180

Reorder the terms:
(-7 + 6x)(-8 + 9x) = 180

Multiply (-7 + 6x) * (-8 + 9x)
(-7(-8 + 9x) + 6x * (-8 + 9x)) = 180
((-8 * -7 + 9x * -7) + 6x * (-8 + 9x)) = 180
((56 + -63x) + 6x * (-8 + 9x)) = 180
(56 + -63x + (-8 * 6x + 9x * 6x)) = 180
(56 + -63x + (-48x + 54x2)) = 180

Combine like terms: -63x + -48x = -111x
(56 + -111x + 54x2) = 180

Solving
56 + -111x + 54x2 = 180

Solving for variable 'x'.

Reorder the terms:
56 + -180 + -111x + 54x2 = 180 + -180

Combine like terms: 56 + -180 = -124
-124 + -111x + 54x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-124 + -111x + 54x2 = 0

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

Divide each side by '54'.
-2.296296296 + -2.055555556x + x2 = 0

Move the constant term to the right:

Add '2.296296296' to each side of the equation.
-2.296296296 + -2.055555556x + 2.296296296 + x2 = 0 + 2.296296296

Reorder the terms:
-2.296296296 + 2.296296296 + -2.055555556x + x2 = 0 + 2.296296296

Combine like terms: -2.296296296 + 2.296296296 = 0.000000000
0.000000000 + -2.055555556x + x2 = 0 + 2.296296296
-2.055555556x + x2 = 0 + 2.296296296

Combine like terms: 0 + 2.296296296 = 2.296296296
-2.055555556x + x2 = 2.296296296

The x term is -2.055555556x.  Take half its coefficient (-1.027777778).
Square it (1.056327161) and add it to both sides.

Add '1.056327161' to each side of the equation.
-2.055555556x + 1.056327161 + x2 = 2.296296296 + 1.056327161

Reorder the terms:
1.056327161 + -2.055555556x + x2 = 2.296296296 + 1.056327161

Combine like terms: 2.296296296 + 1.056327161 = 3.352623457
1.056327161 + -2.055555556x + x2 = 3.352623457

Factor a perfect square on the left side:
(x + -1.027777778)(x + -1.027777778) = 3.352623457

Calculate the square root of the right side: 1.831017055

Break this problem into two subproblems by setting 
(x + -1.027777778) equal to 1.831017055 and -1.831017055.

Subproblem 1

x + -1.027777778 = 1.831017055 Simplifying x + -1.027777778 = 1.831017055 Reorder the terms: -1.027777778 + x = 1.831017055 Solving -1.027777778 + x = 1.831017055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.027777778' to each side of the equation. -1.027777778 + 1.027777778 + x = 1.831017055 + 1.027777778 Combine like terms: -1.027777778 + 1.027777778 = 0.000000000 0.000000000 + x = 1.831017055 + 1.027777778 x = 1.831017055 + 1.027777778 Combine like terms: 1.831017055 + 1.027777778 = 2.858794833 x = 2.858794833 Simplifying x = 2.858794833

Subproblem 2

x + -1.027777778 = -1.831017055 Simplifying x + -1.027777778 = -1.831017055 Reorder the terms: -1.027777778 + x = -1.831017055 Solving -1.027777778 + x = -1.831017055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.027777778' to each side of the equation. -1.027777778 + 1.027777778 + x = -1.831017055 + 1.027777778 Combine like terms: -1.027777778 + 1.027777778 = 0.000000000 0.000000000 + x = -1.831017055 + 1.027777778 x = -1.831017055 + 1.027777778 Combine like terms: -1.831017055 + 1.027777778 = -0.803239277 x = -0.803239277 Simplifying x = -0.803239277

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.858794833, -0.803239277}

See similar equations:

| .7p=p-250 | | .3p=p-250 | | 2.10x-x=648 | | 20x-5=7+17x | | 1/2x+1/3y+8/31/2x+2y=6 | | -31=-6p-7p | | 8.67/10^2 | | 2(2m-3)=6m+12 | | 2x-5=5x+6 | | 180-(12x+12)= | | 625x=5x^2 | | (6x+3y)(8x^2-4xy+2y^2)=0 | | [7x+4]=18 | | 6*.05n+.25q=4.4 | | 1/6(3/4x-2)-1/5 | | 1/2x+1/3y+8/3 | | (7/(X+2))-6=(5X+14)/(X+2) | | [4x+5]=-1 | | 6n+.25=4.4 | | 4(2bx-3y)=7(bx+2) | | -15x=-195 | | 6(3/4x-2)=-1/5 | | 5x/12=6/13 | | 6n+q=4.4 | | 2y-4=5y+20 | | -v+5+4v=1+v+3 | | x-1=6y | | [5x-1]=4 | | 3/4j=12 | | 3-2(k-1)=17 | | 3x-4=24x+3 | | 9x=28+5x |

Equations solver categories