Given:
[tex]4x^2-15x=4[/tex]
Let's solve the equation by factoring,
Subtract 4 from both sides:
[tex]\begin{gathered} 4x^2-15x-4=4-4 \\ \\ 4x^2-15x-4=0 \end{gathered}[/tex]
Now, let's factor by grouping.
Rewrite -15x as (x - 16x):
[tex]4x^2+x-16x-4=0[/tex]
Now we have two groups:
[tex](4x^2+x)-16x-4=0[/tex]
Factor out x from the first group and factor out -4 from the second group:
[tex]x(4x+1)-4(4x+1)=0[/tex]
Thus, we have the factors:
[tex](x-4)(4x+1)=0[/tex]
Set each factor to zero and solve for x:
[tex]\begin{gathered} x-4=0 \\ Add\text{ 4 to both sides:} \\ x-4+4=0+4 \\ x=4 \\ \\ \\ 4x+1=0 \\ Subtract\text{ 1from both sides:} \\ 4x+1-1=0-1 \\ 4x=-1 \\ Divde\text{ both sides by 4:} \\ \frac{4x}{4}=-\frac{1}{4} \\ x=-\frac{1}{4} \end{gathered}[/tex]
Therefore, the solutions are:
[tex]x=-\frac{1}{4}\text{ or x = 4}[/tex]
ANSWER: D
[tex]x=-\frac{1}{4}\text{ or x = 4}[/tex]
