(5+w)*(4w-6)=0

Solution for (5+w)*(4w-6)=0 equation:

Simplifying
(5 + w)(4w + -6) = 0

Reorder the terms:
(5 + w)(-6 + 4w) = 0

Multiply (5 + w) * (-6 + 4w)
(5(-6 + 4w) + w(-6 + 4w)) = 0
((-6 * 5 + 4w * 5) + w(-6 + 4w)) = 0
((-30 + 20w) + w(-6 + 4w)) = 0
(-30 + 20w + (-6 * w + 4w * w)) = 0
(-30 + 20w + (-6w + 4w2)) = 0

Combine like terms: 20w + -6w = 14w
(-30 + 14w + 4w2) = 0

Solving
-30 + 14w + 4w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + 7w + 2w2) = 0

Factor a trinomial.
2((-5 + -1w)(3 + -2w)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -1w)' equal to zero and attempt to solve:

Simplifying
-5 + -1w = 0

Solving
-5 + -1w = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1w = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1w = 0 + 5
-1w = 0 + 5

Combine like terms: 0 + 5 = 5
-1w = 5

Divide each side by '-1'.
w = -5

Simplifying
w = -5
Subproblem 2
Set the factor '(3 + -2w)' equal to zero and attempt to solve:

Simplifying
3 + -2w = 0

Solving
3 + -2w = 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 + -2w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2w = 0 + -3
-2w = 0 + -3

Combine like terms: 0 + -3 = -3
-2w = -3

Divide each side by '-2'.
w = 1.5

Simplifying
w = 1.5
Solution
w = {-5, 1.5}