w^2(4w^2-28w+49)=0

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Solution for w^2(4w^2-28w+49)=0 equation: 


Simplifying
w2(4w2 + -28w + 49) = 0

Reorder the terms:
w2(49 + -28w + 4w2) = 0
(49 * w2 + -28w * w2 + 4w2 * w2) = 0
(49w2 + -28w3 + 4w4) = 0

Solving
49w2 + -28w3 + 4w4 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), 'w2'.
w2(49 + -28w + 4w2) = 0

Factor a trinomial.
w2((7 + -2w)(7 + -2w)) = 0


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 '(7 + -2w)' equal to zero and attempt to solve:

Simplifying
7 + -2w = 0

Solving
7 + -2w = 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 + -2w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2w = 0 + -7
-2w = 0 + -7

Combine like terms: 0 + -7 = -7
-2w = -7

Divide each side by '-2'.
w = 3.5

Simplifying
w = 3.5

Subproblem 3
Set the factor '(7 + -2w)' equal to zero and attempt to solve:

Simplifying
7 + -2w = 0

Solving
7 + -2w = 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 + -2w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2w = 0 + -7
-2w = 0 + -7

Combine like terms: 0 + -7 = -7
-2w = -7

Divide each side by '-2'.
w = 3.5

Simplifying
w = 3.5
Solution
w = {0, 3.5, 3.5}

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