Step/Answer:
The mistake begins at the line 3 where distrubting 2 in the expression. line 1 and line 2 both are correct. But line 3 is wrong.
[tex]2 {x}^{2} + 2x - 2 = 2 {x}^{2} - 18 \\ 2 {x}^{2} + 2x - 2 - 2 {x}^{2} + 18 = 0 \\ 2x - 2 + 18 = 0 \\ 2x + 16 = 0 \\ 2x = - 16 \\ x = - 8[/tex]
[tex]2( {x}^{2} - 9) = (2 \times {x}^{2} ) + (2 \times ( - 9)[/tex]
From line 3, you forgot to distribute 2 in -9.
