x(x+7)(3-6x)>=0

Solve the inequality x(x+7)(3-6x) ≥ 0.

Factor roots: x = -7, 0, 1/2.

Sign chart (test intervals):

• (-∞, -7): positive
• (-7, 0): negative
• (0, 1/2): positive
• (1/2, ∞): negative

Zeros (where expression is 0) at x = -7, 0, 1/2, so include them.

Solution set: (-∞, -7] ∪ [0, 1/2]