Can someone please explain how to solve this problem fast! thanks

[tex]\sf 6b^2-5b=4[/tex]

Subtract 4 to both sides:

[tex]\sf 6b^2-5b-4=0[/tex]

Factor:

We want to find out what two numbers will multiply to get [tex]\sf ac[/tex] and add up to get [tex]\sf b[/tex]. Our quadratic is in the form of [tex]\sf ax^2+bx+c[/tex]. So in this case, a is 6, b is -5, and c is -4. [tex]\sf ac\rightarrow (6)(-4)\rightarrow -24[/tex]. And we know that b is -5, so we want to find two numbers that will multiply to get -24 and add up to get -5. These two numbers are 3 and -8. Rewrite -5b in the quadratic with these:

[tex]\sf 6b^2+3b-8b-4=0[/tex]

Now factor them separately:

[tex]\sf (6b^2+3b)+(-8b-4)=0\rightarrow 3b(2b+1)-4(2b+1)=0[/tex]

As you can see (2b + 1) is common for both terms, so we can just group the beginning of the terms together to get:

[tex]\sf (3b-4)(2b+1)=0[/tex]

Set each one equal to 0 and solve for 'b':

[tex]\sf 3b-4=0[/tex]

Add 4 to both sides:

[tex]\sf 3b=4[/tex]

Divide 3 to both sides:

[tex]\boxed{\sf b=\dfrac{4}{3}}[/tex]

[tex]\sf 2b+1=0[/tex]

Subtract 1 to both sides:

[tex]\sf 2b=-1[/tex]

Divide 2 to both sides:

[tex]\boxed{\sf b=-\dfrac{1}{2}}[/tex]