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

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

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

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

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