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

Solution for (1+w)(4w-6)=0 equation:

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

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

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

Combine like terms: 4w + -6w = -2w
(-6 + -2w + 4w2) = 0

Solving
-6 + -2w + 4w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -1w + 2w2) = 0

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

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

Simplifying
-1 + -1w = 0

Solving
-1 + -1w = 0

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

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

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

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

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

Simplifying
w = -1
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 = {-1, 1.5}