(5w-3)(6+w)=0

Solution for (5w-3)(6+w)=0 equation:

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

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

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

Combine like terms: -3w + 30w = 27w
(-18 + 27w + 5w2) = 0

Solving
-18 + 27w + 5w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-6 + -1w)(3 + -5w) = 0

Subproblem 1
Set the factor '(-6 + -1w)' equal to zero and attempt to solve:

Simplifying
-6 + -1w = 0

Solving
-6 + -1w = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1w = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1w = 0 + 6
-1w = 0 + 6

Combine like terms: 0 + 6 = 6
-1w = 6

Divide each side by '-1'.
w = -6

Simplifying
w = -6
Subproblem 2
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 = {-6, 0.6}