(7-w)(4w+6)=0

Solution for (7-w)(4w+6)=0 equation:

Simplifying
(7 + -1w)(4w + 6) = 0

Reorder the terms:
(7 + -1w)(6 + 4w) = 0

Multiply (7 + -1w) * (6 + 4w)
(7(6 + 4w) + -1w * (6 + 4w)) = 0
((6 * 7 + 4w * 7) + -1w * (6 + 4w)) = 0
((42 + 28w) + -1w * (6 + 4w)) = 0
(42 + 28w + (6 * -1w + 4w * -1w)) = 0
(42 + 28w + (-6w + -4w2)) = 0

Combine like terms: 28w + -6w = 22w
(42 + 22w + -4w2) = 0

Solving
42 + 22w + -4w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(21 + 11w + -2w2) = 0

Factor a trinomial.
2((7 + -1w)(3 + 2w)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(7 + -1w)' equal to zero and attempt to solve:

Simplifying
7 + -1w = 0

Solving
7 + -1w = 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 + -1w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1w = 0 + -7
-1w = 0 + -7

Combine like terms: 0 + -7 = -7
-1w = -7

Divide each side by '-1'.
w = 7

Simplifying
w = 7
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 = {7, -1.5}