(7w-2)(2w+1)=0

Solution for (7w-2)(2w+1)=0 equation:

Simplifying
(7w + -2)(2w + 1) = 0

Reorder the terms:
(-2 + 7w)(2w + 1) = 0

Reorder the terms:
(-2 + 7w)(1 + 2w) = 0

Multiply (-2 + 7w) * (1 + 2w)
(-2(1 + 2w) + 7w * (1 + 2w)) = 0
((1 * -2 + 2w * -2) + 7w * (1 + 2w)) = 0
((-2 + -4w) + 7w * (1 + 2w)) = 0
(-2 + -4w + (1 * 7w + 2w * 7w)) = 0
(-2 + -4w + (7w + 14w2)) = 0

Combine like terms: -4w + 7w = 3w
(-2 + 3w + 14w2) = 0

Solving
-2 + 3w + 14w2 = 0

Solving for variable 'w'.

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

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

Simplifying
-1 + -2w = 0

Solving
-1 + -2w = 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 + -2w = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2w = 0 + 1
-2w = 0 + 1

Combine like terms: 0 + 1 = 1
-2w = 1

Divide each side by '-2'.
w = -0.5

Simplifying
w = -0.5
Subproblem 2
Set the factor '(2 + -7w)' equal to zero and attempt to solve:

Simplifying
2 + -7w = 0

Solving
2 + -7w = 0

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

Add '-2' to each side of the equation.
2 + -2 + -7w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -7w = 0 + -2
-7w = 0 + -2

Combine like terms: 0 + -2 = -2
-7w = -2

Divide each side by '-7'.
w = 0.2857142857

Simplifying
w = 0.2857142857
Solution
w = {-0.5, 0.2857142857}