4w^2+12w+9=21

Solution for 4w^2+12w+9=21 equation:

Simplifying
4w2 + 12w + 9 = 21

Reorder the terms:
9 + 12w + 4w2 = 21

Solving
9 + 12w + 4w2 = 21

Solving for variable 'w'.

Reorder the terms:
9 + -21 + 12w + 4w2 = 21 + -21

Combine like terms: 9 + -21 = -12
-12 + 12w + 4w2 = 21 + -21

Combine like terms: 21 + -21 = 0
-12 + 12w + 4w2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-3 + 3w + w2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-3 + 3w + w2)' equal to zero and attempt to solve:

Simplifying
-3 + 3w + w2 = 0

Solving
-3 + 3w + w2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = 3 + 2.25

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

Combine like terms: 3 + 2.25 = 5.25
2.25 + 3w + w2 = 5.25

Factor a perfect square on the left side:
(w + 1.5)(w + 1.5) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(w + 1.5) equal to 2.291287847 and -2.291287847.

Subproblem 1
w + 1.5 = 2.291287847

Simplifying
w + 1.5 = 2.291287847

Reorder the terms:
1.5 + w = 2.291287847

Solving
1.5 + w = 2.291287847

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 = 2.291287847 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + w = 2.291287847 + -1.5
w = 2.291287847 + -1.5

Combine like terms: 2.291287847 + -1.5 = 0.791287847
w = 0.791287847

Simplifying
w = 0.791287847

Subproblem 2
w + 1.5 = -2.291287847

Simplifying
w + 1.5 = -2.291287847

Reorder the terms:
1.5 + w = -2.291287847

Solving
1.5 + w = -2.291287847

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 = -2.291287847 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + w = -2.291287847 + -1.5
w = -2.291287847 + -1.5

Combine like terms: -2.291287847 + -1.5 = -3.791287847
w = -3.791287847

Simplifying
w = -3.791287847

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {0.791287847, -3.791287847}
Solution
w = {0.791287847, -3.791287847}