6b^2+6b-16=0

Simple and best practice solution for 6b^2+6b-16=0 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 6b^2+6b-16=0 equation: 


Simplifying
6b2 + 6b + -16 = 0

Reorder the terms:
-16 + 6b + 6b2 = 0

Solving
-16 + 6b + 6b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + 3b + 3b2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-8 + 3b + 3b2)' equal to zero and attempt to solve:

Simplifying
-8 + 3b + 3b2 = 0

Solving
-8 + 3b + 3b2 = 0

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

Divide each side by '3'.
-2.666666667 + b + b2 = 0

Move the constant term to the right:

Add '2.666666667' to each side of the equation.
-2.666666667 + b + 2.666666667 + b2 = 0 + 2.666666667

Reorder the terms:
-2.666666667 + 2.666666667 + b + b2 = 0 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + b + b2 = 0 + 2.666666667
b + b2 = 0 + 2.666666667

Combine like terms: 0 + 2.666666667 = 2.666666667
b + b2 = 2.666666667

The b term is b.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + b2 = 2.666666667 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + b2 = 2.666666667 + 0.25

Combine like terms: 2.666666667 + 0.25 = 2.916666667
1.25 + b2 = 2.916666667

Factor a perfect square on the left side:
(b + 0.5)(b + 0.5) = 2.916666667

Calculate the square root of the right side: 1.707825128

Break this problem into two subproblems by setting 
(b + 0.5) equal to 1.707825128 and -1.707825128.


Subproblem 1
b + 0.5 = 1.707825128

Simplifying
b + 0.5 = 1.707825128

Reorder the terms:
0.5 + b = 1.707825128

Solving
0.5 + b = 1.707825128

Solving for variable 'b'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + b = 1.707825128 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + b = 1.707825128 + -0.5
b = 1.707825128 + -0.5

Combine like terms: 1.707825128 + -0.5 = 1.207825128
b = 1.207825128

Simplifying
b = 1.207825128


Subproblem 2
b + 0.5 = -1.707825128

Simplifying
b + 0.5 = -1.707825128

Reorder the terms:
0.5 + b = -1.707825128

Solving
0.5 + b = -1.707825128

Solving for variable 'b'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + b = -1.707825128 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + b = -1.707825128 + -0.5
b = -1.707825128 + -0.5

Combine like terms: -1.707825128 + -0.5 = -2.207825128
b = -2.207825128

Simplifying
b = -2.207825128


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {1.207825128, -2.207825128}
Solution
b = {1.207825128, -2.207825128}

See similar equations:

| 84=4*6*3+2*3*h | | 8x^4+8x^3-x-1=0 | | 3x=21+2y | | 45x-10x= | | 2y+12-3y+12= | | 15+2y=7y | | -12+x=4.55 | | 0.44x=0.5y | | -6x-3=-2 | | 27a^3c^4+b^3=0 | | -3n+6n=0 | | 6-x=9-3x | | -7(1-4m)=13(2m-9) | | 2x+120=50 | | 5x^2-39x-100=0 | | b-2/5=3 | | 5x+2(x+7)=77 | | (-8,-8),(5,14)= | | -x-2=-44+5 | | 13+n=15 | | x^2+20x+55=180 | | p-(s-t)=p | | 7n^2+46n+7n^2=0 | | ln(2-3x)=0 | | 2a^2+17ab+30b^2= | | K*2-7p-18=0 | | 3(7-8x)+2(x-1)=-8(3+x)+2(4-x) | | a-b+(-a)-3b= | | 2*2+3*3-4+3*5=14 | | 3-6x=3(1+2a) | | 9m^2=0 | | 8=logx |

Equations solver categories