-3w^2(5w+3)(6w+7)=

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Solution for -3w^2(5w+3)(6w+7)= equation: 


Simplifying
-3w2(5w + 3)(6w + 7) = 0

Reorder the terms:
-3w2(3 + 5w)(6w + 7) = 0

Reorder the terms:
-3w2(3 + 5w)(7 + 6w) = 0

Multiply (3 + 5w) * (7 + 6w)
-3w2(3(7 + 6w) + 5w * (7 + 6w)) = 0
-3w2((7 * 3 + 6w * 3) + 5w * (7 + 6w)) = 0
-3w2((21 + 18w) + 5w * (7 + 6w)) = 0
-3w2(21 + 18w + (7 * 5w + 6w * 5w)) = 0
-3w2(21 + 18w + (35w + 30w2)) = 0

Combine like terms: 18w + 35w = 53w
-3w2(21 + 53w + 30w2) = 0
(21 * -3w2 + 53w * -3w2 + 30w2 * -3w2) = 0
(-63w2 + -159w3 + -90w4) = 0

Solving
-63w2 + -159w3 + -90w4 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '-3w2'.
-3w2(21 + 53w + 30w2) = 0

Factor a trinomial.
-3w2((7 + 6w)(3 + 5w)) = 0

Ignore the factor -3.

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 + 6w)' equal to zero and attempt to solve:

Simplifying
7 + 6w = 0

Solving
7 + 6w = 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 + 6w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 6w = 0 + -7
6w = 0 + -7

Combine like terms: 0 + -7 = -7
6w = -7

Divide each side by '6'.
w = -1.166666667

Simplifying
w = -1.166666667

Subproblem 3
Set the factor '(3 + 5w)' equal to zero and attempt to solve:

Simplifying
3 + 5w = 0

Solving
3 + 5w = 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 + 5w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5w = 0 + -3
5w = 0 + -3

Combine like terms: 0 + -3 = -3
5w = -3

Divide each side by '5'.
w = -0.6

Simplifying
w = -0.6
Solution
w = {0, -1.166666667, -0.6}

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