`a)`
`3x^2 - 15x = 0`
`⇔ 3x(x - 5) = 0`
`⇒ x(x - 5) = 0`
`⇒` \(\left[ \begin{array}{l}x = 0\\x = 5\end{array} \right.\)
`b)`
`x(x - 4) + (x - 4) = 0`
`⇔ (x - 4)(x + 1) = 0`
`⇒ `\(\left[ \begin{array}{l}x = 4\\x = -1\end{array} \right.\)
`c)`
`x^2 + 11x + 30 = 0`
`⇔ x^2 + 5x + 6x + 30 = 0`
`⇒ x(x + 5) + 6(x + 5) = 0`
`⇒ (x + 5)(x + 6) = 0`
`⇒` \(\left[ \begin{array}{l}x = -5\\x = -6\end{array} \right.\)
`d)`
`x^4 - 6x^2 + 7x - 6 = 0`
`⇔ x^4 - 2x^3 + 2x^3 - 4x^2 - 2x^2 + 4x + 3x - 6 = 0`
`⇔ x^3(x - 2) + 2x^2(x - 2) - 2x(x - 2) + 3(x - 2) = 0`
`⇔ (x - 2)(x^3 + 2x^2 - 2x + 3) = 0`
`⇒ x - 2 = 0` `(do x^3 + 2x^2 - 2x + 3 > 0)`
`⇒ x = 2`