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1.

[tex]12 - v(v - 3) = (6 - v)(v + 2) \\ \\ 12 - {v}^{2} + 3v = 4v + 12 - {v}^{2} \\ \\ {v }^{2} - {v}^{2} + 3v - 4v = 12 - 12 \\ \\ - v = 0 \\ \\ v = 0[/tex]

2.

[tex](s + 4)(s + 1) = s - (s - 2)(2 - s) \\ \\ {s}^{2} + 5s + 4 = s - (4s - {s}^{2} - 4) \\ \\ {s}^{2} + 5s + 4 = - 3s + {s}^{2} + 4 \\ \\ {s}^{2} + 5s + 3s - {s}^{2} = 4 - 4 \\ \\ 8s = 0 \\ \\ s = 0[/tex]

1.

[tex](3s - 1)(5s + 4) - 15 {s}^{2} = 17 \\ \\ 15 {s}^{2} + 7s - 4 - 15 {s}^{2} = 17 \\ \\ 7s = 21 \\ \\ s = 3[/tex]

2.

[tex](1 - 2g)(1 - 3g) = (6g - 1)g - 1 \\ \\ 1 - 5g + 6 {g}^{2} = 6 {g}^{2} - g - 1 \\ \\ 6 {g}^{2} - 6 {g}^{2} - 5g + g = - 2 \\ \\ - 4g = - 2 \\ \\ g = \frac{1}{2} [/tex]