3w^2+24w+21=0

Solution for 3w^2+24w+21=0 equation:

Simplifying
3w2 + 24w + 21 = 0

Reorder the terms:
21 + 24w + 3w2 = 0

Solving
21 + 24w + 3w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '3'.
3(7 + 8w + w2) = 0

Factor a trinomial.
3((7 + w)(1 + w)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(7 + w)' equal to zero and attempt to solve:

Simplifying
7 + w = 0

Solving
7 + w = 0

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

Add '-7' to each side of the equation.
7 + -7 + w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + w = 0 + -7
w = 0 + -7

Combine like terms: 0 + -7 = -7
w = -7

Simplifying
w = -7
Subproblem 2
Set the factor '(1 + w)' equal to zero and attempt to solve:

Simplifying
1 + w = 0

Solving
1 + w = 0

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

Add '-1' to each side of the equation.
1 + -1 + w = 0 + -1

Combine like terms: 1 + -1 = 0
0 + w = 0 + -1
w = 0 + -1

Combine like terms: 0 + -1 = -1
w = -1

Simplifying
w = -1
Solution
w = {-7, -1}