(2w+6)(5w-4)=0

Solution for (2w+6)(5w-4)=0 equation:

Simplifying
(2w + 6)(5w + -4) = 0

Reorder the terms:
(6 + 2w)(5w + -4) = 0

Reorder the terms:
(6 + 2w)(-4 + 5w) = 0

Multiply (6 + 2w) * (-4 + 5w)
(6(-4 + 5w) + 2w * (-4 + 5w)) = 0
((-4 * 6 + 5w * 6) + 2w * (-4 + 5w)) = 0
((-24 + 30w) + 2w * (-4 + 5w)) = 0
(-24 + 30w + (-4 * 2w + 5w * 2w)) = 0
(-24 + 30w + (-8w + 10w2)) = 0

Combine like terms: 30w + -8w = 22w
(-24 + 22w + 10w2) = 0

Solving
-24 + 22w + 10w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + 11w + 5w2) = 0

Factor a trinomial.
2((-3 + -1w)(4 + -5w)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -1w)' equal to zero and attempt to solve:

Simplifying
-3 + -1w = 0

Solving
-3 + -1w = 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 + -1w = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1w = 0 + 3
-1w = 0 + 3

Combine like terms: 0 + 3 = 3
-1w = 3

Divide each side by '-1'.
w = -3

Simplifying
w = -3
Subproblem 2
Set the factor '(4 + -5w)' equal to zero and attempt to solve:

Simplifying
4 + -5w = 0

Solving
4 + -5w = 0

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

Add '-4' to each side of the equation.
4 + -4 + -5w = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5w = 0 + -4
-5w = 0 + -4

Combine like terms: 0 + -4 = -4
-5w = -4

Divide each side by '-5'.
w = 0.8

Simplifying
w = 0.8
Solution
w = {-3, 0.8}