3w(3w+16)=-36

Simple and best practice solution for 3w(3w+16)=-36 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 3w(3w+16)=-36 equation: 


Simplifying
3w(3w + 16) = -36

Reorder the terms:
3w(16 + 3w) = -36
(16 * 3w + 3w * 3w) = -36
(48w + 9w2) = -36

Solving
48w + 9w2 = -36

Solving for variable 'w'.

Reorder the terms:
36 + 48w + 9w2 = -36 + 36

Combine like terms: -36 + 36 = 0
36 + 48w + 9w2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(12 + 16w + 3w2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(12 + 16w + 3w2)' equal to zero and attempt to solve:

Simplifying
12 + 16w + 3w2 = 0

Solving
12 + 16w + 3w2 = 0

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

Divide each side by '3'.
4 + 5.333333333w + w2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 5.333333333w + -4 + w2 = 0 + -4

Reorder the terms:
4 + -4 + 5.333333333w + w2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 5.333333333w + w2 = 0 + -4
5.333333333w + w2 = 0 + -4

Combine like terms: 0 + -4 = -4
5.333333333w + w2 = -4

The w term is 5.333333333w.  Take half its coefficient (2.666666667).
Square it (7.111111113) and add it to both sides.

Add '7.111111113' to each side of the equation.
5.333333333w + 7.111111113 + w2 = -4 + 7.111111113

Reorder the terms:
7.111111113 + 5.333333333w + w2 = -4 + 7.111111113

Combine like terms: -4 + 7.111111113 = 3.111111113
7.111111113 + 5.333333333w + w2 = 3.111111113

Factor a perfect square on the left side:
(w + 2.666666667)(w + 2.666666667) = 3.111111113

Calculate the square root of the right side: 1.763834208

Break this problem into two subproblems by setting 
(w + 2.666666667) equal to 1.763834208 and -1.763834208.


Subproblem 1
w + 2.666666667 = 1.763834208

Simplifying
w + 2.666666667 = 1.763834208

Reorder the terms:
2.666666667 + w = 1.763834208

Solving
2.666666667 + w = 1.763834208

Solving for variable 'w'.

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

Add '-2.666666667' to each side of the equation.
2.666666667 + -2.666666667 + w = 1.763834208 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + w = 1.763834208 + -2.666666667
w = 1.763834208 + -2.666666667

Combine like terms: 1.763834208 + -2.666666667 = -0.902832459
w = -0.902832459

Simplifying
w = -0.902832459


Subproblem 2
w + 2.666666667 = -1.763834208

Simplifying
w + 2.666666667 = -1.763834208

Reorder the terms:
2.666666667 + w = -1.763834208

Solving
2.666666667 + w = -1.763834208

Solving for variable 'w'.

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

Add '-2.666666667' to each side of the equation.
2.666666667 + -2.666666667 + w = -1.763834208 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + w = -1.763834208 + -2.666666667
w = -1.763834208 + -2.666666667

Combine like terms: -1.763834208 + -2.666666667 = -4.430500875
w = -4.430500875

Simplifying
w = -4.430500875


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {-0.902832459, -4.430500875}
Solution
w = {-0.902832459, -4.430500875}

See similar equations:

| 9h^2+32h=0 | | (2x+4y)(2x-4y)= | | Y=5cos(x-60)+3cosx | | 5.6=5x+4.2 | | 2f^2-5f-12=0 | | Y=5cps(x-60)+3cosx | | 7x-58.8=x | | 3(x-7.3)=8.7 | | G=16-1/20100 | | f(x)=3x^2-18x+24 | | X^2+16X+64X=0 | | 6x+8.14=4x+12 | | .155x=24-x+.25 | | X-2=1.95 | | K^2+16k+16=6k | | -3y=2.16 | | X+2.6=6.8 | | x5/3 | | Y-11/23=-7/23 | | y=2x-1/3 | | 6n^2-7n+2=4-5n+5n^2 | | 0=16t^2*32t | | (2y-4)(2y-4)-36=(6-2y)(6-2y) | | 6x^2+5x=144 | | 3x^2-6=129 | | 32=3x+4y | | x^2+13x+6=-x^2+4x+2 | | 8r^2-2=798 | | 4x^2*2x=8x^3 | | x(2x+2)+x(2x+4)=4x+72 | | 7x-60=-18 | | 3x+50=6x+20 |

Equations solver categories