6w^2(3+w)(-3+w)=

Solution for 6w^2(3+w)(-3+w)= equation:

Simplifying
6w2(3 + w)(-3 + w) = 0

Multiply (3 + w) * (-3 + w)
6w2(3(-3 + w) + w(-3 + w)) = 0
6w2((-3 * 3 + w * 3) + w(-3 + w)) = 0
6w2((-9 + 3w) + w(-3 + w)) = 0
6w2(-9 + 3w + (-3 * w + w * w)) = 0
6w2(-9 + 3w + (-3w + w2)) = 0

Combine like terms: 3w + -3w = 0
6w2(-9 + 0 + w2) = 0
6w2(-9 + w2) = 0
(-9 * 6w2 + w2 * 6w2) = 0
(-54w2 + 6w4) = 0

Solving
-54w2 + 6w4 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '6w2'.
6w2(-9 + w2) = 0

Factor a difference between two squares.
6w2((3 + w)(-3 + w)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor 'w2' equal to zero and attempt to solve:

Simplifying
w2 = 0

Solving
w2 = 0

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

Simplifying
w2 = 0

Take the square root of each side:
w = {0}
Subproblem 2
Set the factor '(3 + w)' equal to zero and attempt to solve:

Simplifying
3 + w = 0

Solving
3 + w = 0

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

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

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

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

Simplifying
w = -3
Subproblem 3
Set the factor '(-3 + w)' equal to zero and attempt to solve:

Simplifying
-3 + w = 0

Solving
-3 + w = 0

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

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

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

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

Simplifying
w = 3
Solution
w = {0, -3, 3}