(2x+6)(3x-5)=8

Simple and best practice solution for (2x+6)(3x-5)=8 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 (2x+6)(3x-5)=8 equation: 


Simplifying
(2x + 6)(3x + -5) = 8

Reorder the terms:
(6 + 2x)(3x + -5) = 8

Reorder the terms:
(6 + 2x)(-5 + 3x) = 8

Multiply (6 + 2x) * (-5 + 3x)
(6(-5 + 3x) + 2x * (-5 + 3x)) = 8
((-5 * 6 + 3x * 6) + 2x * (-5 + 3x)) = 8
((-30 + 18x) + 2x * (-5 + 3x)) = 8
(-30 + 18x + (-5 * 2x + 3x * 2x)) = 8
(-30 + 18x + (-10x + 6x2)) = 8

Combine like terms: 18x + -10x = 8x
(-30 + 8x + 6x2) = 8

Solving
-30 + 8x + 6x2 = 8

Solving for variable 'x'.

Reorder the terms:
-30 + -8 + 8x + 6x2 = 8 + -8

Combine like terms: -30 + -8 = -38
-38 + 8x + 6x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-38 + 8x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-19 + 4x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-19 + 4x + 3x2)' equal to zero and attempt to solve:

Simplifying
-19 + 4x + 3x2 = 0

Solving
-19 + 4x + 3x2 = 0

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

Divide each side by '3'.
-6.333333333 + 1.333333333x + x2 = 0

Move the constant term to the right:

Add '6.333333333' to each side of the equation.
-6.333333333 + 1.333333333x + 6.333333333 + x2 = 0 + 6.333333333

Reorder the terms:
-6.333333333 + 6.333333333 + 1.333333333x + x2 = 0 + 6.333333333

Combine like terms: -6.333333333 + 6.333333333 = 0.000000000
0.000000000 + 1.333333333x + x2 = 0 + 6.333333333
1.333333333x + x2 = 0 + 6.333333333

Combine like terms: 0 + 6.333333333 = 6.333333333
1.333333333x + x2 = 6.333333333

The x term is 1.333333333x.  Take half its coefficient (0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
1.333333333x + 0.4444444442 + x2 = 6.333333333 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333x + x2 = 6.333333333 + 0.4444444442

Combine like terms: 6.333333333 + 0.4444444442 = 6.7777777772
0.4444444442 + 1.333333333x + x2 = 6.7777777772

Factor a perfect square on the left side:
(x + 0.6666666665)(x + 0.6666666665) = 6.7777777772

Calculate the square root of the right side: 2.603416559

Break this problem into two subproblems by setting 
(x + 0.6666666665) equal to 2.603416559 and -2.603416559.


Subproblem 1
x + 0.6666666665 = 2.603416559

Simplifying
x + 0.6666666665 = 2.603416559

Reorder the terms:
0.6666666665 + x = 2.603416559

Solving
0.6666666665 + x = 2.603416559

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + x = 2.603416559 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + x = 2.603416559 + -0.6666666665
x = 2.603416559 + -0.6666666665

Combine like terms: 2.603416559 + -0.6666666665 = 1.9367498925
x = 1.9367498925

Simplifying
x = 1.9367498925


Subproblem 2
x + 0.6666666665 = -2.603416559

Simplifying
x + 0.6666666665 = -2.603416559

Reorder the terms:
0.6666666665 + x = -2.603416559

Solving
0.6666666665 + x = -2.603416559

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + x = -2.603416559 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + x = -2.603416559 + -0.6666666665
x = -2.603416559 + -0.6666666665

Combine like terms: -2.603416559 + -0.6666666665 = -3.2700832255
x = -3.2700832255

Simplifying
x = -3.2700832255


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.9367498925, -3.2700832255}
Solution
x = {1.9367498925, -3.2700832255}

See similar equations:

| g(x)=4-2whatisg(x-4) | | 8/60,328 | | 16=-6w+2(w+4) | | ln(x^2+3)-lnx^2=1 | | (2hk^3)^3/(-h^2k^2)^2 | | 2/3x-5=21 | | 12/80 | | x-0.54=7 | | (1+x)yDX+(1-y)xday=0 | | 9x=113+5y | | p+4=-1 | | Y^2=361 | | x-0.12=3.2 | | 5x^3/10 | | 1667+0+x=1.3x | | 2y=x+e | | ln(7-x)+ln(1-x)=ln(25-x) | | h(4x)=3x^2+7 | | 20x^6+10x^3+50= | | 1667+500+x=1.3x | | 3334+1000+x=1.3x | | 4(x+3)=vx+42 | | (4x+12)(x-1)= | | -1/5•-10 | | 67-y=26 | | log(2x+1)=2+log(x-2) | | x=94.02-0.13x | | x(0.13)+X=94.02 | | 8x^3-13x^2+6x=0 | | 5n+1=31 | | (-14xy^2)/(21y^2) | | 8m-11=-6+9m |

Equations solver categories