Answer:
x = -9/2 or -5/3
Step-by-step explanation:
The given equation is recognizable as a quadratic in the expression (2x+4). It may be more easily solved by substituting a variable for that expression.
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Let z = 2x+4. Then the equation becomes ...
6z² = z +2
6z^2 -z -2 = 0
This equation can be factored by finding factors of (6)(-2) that total -1.
(6z -4)(6z +3)/6 = 0
(3z -2)(2z +1) = 0 . . . . . eliminate the fraction
The values of z that make these factors zero are ...
3z -2 = 0 ⇒ z = 2/3
2z +1 = 0 ⇒ z = -1/2
The relation between x and z tells us ...
z = 2x +4
(z -4)/2 = x
For the values of z we have, the corresponding x-values are ...
z = 2/3 ⇒ (2/3 -4)/2 = x = -10/6 = -5/3
z = -1/2 ⇒ (-1/2 -4)/2 = x = -9/4
Solutions to the equation are x=-9/4 and x=-5/3.
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Additional comment
Alternatively, the equation could have been expanded to standard form and then factored.
6(4x² +16x +16) = 2x +6
24x² +94x +90 = 0 . . . . put in standard form
12x² +47x +45 = 0 . . . . factor out 2
(4x +9)(3x +5) = 0 . . . . factor (judged harder than the above factoring)
