Answer:
[tex]x = - 5[/tex]
or
[tex]x = 2[/tex]
Step-by-step explanation:
We want to solve ;
[tex] {12}^{ {x}^{2} + 5x - 4} = {12}^{2x + 6} [/tex]
We equate the exponents, because is the same on both sides.
[tex] {x}^{2} + 5x - 4 = 2x + 6[/tex]
We group and rewrite in standard form to get:
[tex] {x}^{2} + 5x - 2x - 4 - 6 = 0[/tex]
[tex]{x}^{2} + 3x- 10= 0[/tex]
[tex] {x}^{2} - 2x + 5x - 10 = 0[/tex]
[tex]x(x - 2) + 5(x - 2) = 0[/tex]
[tex](x + 5)(x - 2) = 0[/tex]
[tex]x = - 5 \: or \: x = 2[/tex]
