w(2w+6)=48

Simple and best practice solution for w(2w+6)=48 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 w(2w+6)=48 equation: 


Simplifying
w(2w + 6) = 48

Reorder the terms:
w(6 + 2w) = 48
(6 * w + 2w * w) = 48
(6w + 2w2) = 48

Solving
6w + 2w2 = 48

Solving for variable 'w'.

Reorder the terms:
-48 + 6w + 2w2 = 48 + -48

Combine like terms: 48 + -48 = 0
-48 + 6w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-24 + 3w + w2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-24 + 3w + w2)' equal to zero and attempt to solve:

Simplifying
-24 + 3w + w2 = 0

Solving
-24 + 3w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + 3w + 24 + w2 = 0 + 24

Reorder the terms:
-24 + 24 + 3w + w2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + 3w + w2 = 0 + 24
3w + w2 = 0 + 24

Combine like terms: 0 + 24 = 24
3w + w2 = 24

The w term is 3w.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3w + 2.25 + w2 = 24 + 2.25

Reorder the terms:
2.25 + 3w + w2 = 24 + 2.25

Combine like terms: 24 + 2.25 = 26.25
2.25 + 3w + w2 = 26.25

Factor a perfect square on the left side:
(w + 1.5)(w + 1.5) = 26.25

Calculate the square root of the right side: 5.123475383

Break this problem into two subproblems by setting 
(w + 1.5) equal to 5.123475383 and -5.123475383.


Subproblem 1
w + 1.5 = 5.123475383

Simplifying
w + 1.5 = 5.123475383

Reorder the terms:
1.5 + w = 5.123475383

Solving
1.5 + w = 5.123475383

Solving for variable 'w'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + w = 5.123475383 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + w = 5.123475383 + -1.5
w = 5.123475383 + -1.5

Combine like terms: 5.123475383 + -1.5 = 3.623475383
w = 3.623475383

Simplifying
w = 3.623475383


Subproblem 2
w + 1.5 = -5.123475383

Simplifying
w + 1.5 = -5.123475383

Reorder the terms:
1.5 + w = -5.123475383

Solving
1.5 + w = -5.123475383

Solving for variable 'w'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + w = -5.123475383 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + w = -5.123475383 + -1.5
w = -5.123475383 + -1.5

Combine like terms: -5.123475383 + -1.5 = -6.623475383
w = -6.623475383

Simplifying
w = -6.623475383


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {3.623475383, -6.623475383}
Solution
w = {3.623475383, -6.623475383}

See similar equations:

| (16x^2yz^3)^(3/4) | | 3sin(2x)-1=1 | | 2X=lnx | | (8x^6w^2-2xw^7)/(2xw^2)= | | -256/-16= | | -15(-9)= | | 2y+2(y-5)=4y+1 | | 99f=27 | | 5x+4(8)=-8 | | 2+M+4=9 | | 6x+6=2(2x+43) | | 8+b+3=16 | | 5+2+w=12 | | 11(x+1)+7x=45353 | | log(2x-1)+log(x-9)=2 | | x^2-11x+10=10 | | 4(h+2)+3=5(-2h+3)-2 | | (4x+3)(6x-1)=9-34 | | 16x^4/2x | | 4.6+1.3x=1.35 | | 2(-3)=-20 | | 1.8-3.7=-4.2x+0.3 | | (1.2x1.2)/((1.68)x(x-1.2)=3.5 | | 6t-9-3t=24 | | 5(X-7)-6x=-28+2(x-2) | | 1.44/(1.68x-1.20)=3 | | 5(x+9)-2(1-x)=1 | | -6y-9=5(y+7) | | 7x-3=x+2 | | 4x+7-9= | | -2.8+-3.6+8.1= | | 2(7x-3)=5x-3 |

Equations solver categories