16b(b+7)=42

Simple and best practice solution for 16b(b+7)=42 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 16b(b+7)=42 equation: 


Simplifying
16b(b + 7) = 42

Reorder the terms:
16b(7 + b) = 42
(7 * 16b + b * 16b) = 42
(112b + 16b2) = 42

Solving
112b + 16b2 = 42

Solving for variable 'b'.

Reorder the terms:
-42 + 112b + 16b2 = 42 + -42

Combine like terms: 42 + -42 = 0
-42 + 112b + 16b2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + 56b + 8b2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-21 + 56b + 8b2)' equal to zero and attempt to solve:

Simplifying
-21 + 56b + 8b2 = 0

Solving
-21 + 56b + 8b2 = 0

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

Divide each side by '8'.
-2.625 + 7b + b2 = 0

Move the constant term to the right:

Add '2.625' to each side of the equation.
-2.625 + 7b + 2.625 + b2 = 0 + 2.625

Reorder the terms:
-2.625 + 2.625 + 7b + b2 = 0 + 2.625

Combine like terms: -2.625 + 2.625 = 0.000
0.000 + 7b + b2 = 0 + 2.625
7b + b2 = 0 + 2.625

Combine like terms: 0 + 2.625 = 2.625
7b + b2 = 2.625

The b term is 7b.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7b + 12.25 + b2 = 2.625 + 12.25

Reorder the terms:
12.25 + 7b + b2 = 2.625 + 12.25

Combine like terms: 2.625 + 12.25 = 14.875
12.25 + 7b + b2 = 14.875

Factor a perfect square on the left side:
(b + 3.5)(b + 3.5) = 14.875

Calculate the square root of the right side: 3.856812155

Break this problem into two subproblems by setting 
(b + 3.5) equal to 3.856812155 and -3.856812155.


Subproblem 1
b + 3.5 = 3.856812155

Simplifying
b + 3.5 = 3.856812155

Reorder the terms:
3.5 + b = 3.856812155

Solving
3.5 + b = 3.856812155

Solving for variable 'b'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + b = 3.856812155 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + b = 3.856812155 + -3.5
b = 3.856812155 + -3.5

Combine like terms: 3.856812155 + -3.5 = 0.356812155
b = 0.356812155

Simplifying
b = 0.356812155


Subproblem 2
b + 3.5 = -3.856812155

Simplifying
b + 3.5 = -3.856812155

Reorder the terms:
3.5 + b = -3.856812155

Solving
3.5 + b = -3.856812155

Solving for variable 'b'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + b = -3.856812155 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + b = -3.856812155 + -3.5
b = -3.856812155 + -3.5

Combine like terms: -3.856812155 + -3.5 = -7.356812155
b = -7.356812155

Simplifying
b = -7.356812155


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {0.356812155, -7.356812155}
Solution
b = {0.356812155, -7.356812155}

See similar equations:

| 4x/-1=64 | | 7(c+4m-28)=56 | | -20=5x/6 | | w=5a+3g | | 2[4t+7-3(2t+3)]=8(3t-4)-7(2t-3) | | 9x^6+3x^5-30x^4=0 | | 10-s/3=s | | 4x+4(-4x+3)=12 | | 2*6*6-3*6+6= | | y=-4x+r | | x/5+11=731 | | 10/4*=25 | | x-8/33=40 | | x+5/3=9 | | r/-2+8=5 | | 500/25= | | 14=k/8+7 | | x=log(8.3) | | p(x)=x^3-5x+1 | | (x^2+144)=0 | | in(x)=log(8.3) | | 8(x/6) | | 8/1*x/6 | | -90-(-29)-38-(52)= | | 3-(4y-7)=(2y+3)-(6y+6) | | x/48=2x+4 | | -y^2+x+6y-4=0 | | 3-(4y-7)=(2y+3) | | ab-9a+3b-27= | | x/24=-56 | | 3x-y=3x+2y | | x/80=11 |

Equations solver categories