Answer: [tex]x=-\frac{5}{4}[/tex] and [tex]x=-2[/tex]
Step-by-step explanation:
To factor an equation in the form of [tex]ax^2+bx+c[/tex] you need to find the value of [tex]ac[/tex]. So first solve for that
[tex](4)(10) = 40[/tex]
Now we need to find two numbers that add up to b and multiply together to make ac. In this case those numbers are 5 and 8 since 5+8=13 and (5)(8)=40
Now split 13x into 5x+8x and solve by grouping
[tex]4x^2+5x+8x+10\\(4x^2+5x)+(8x+10)[/tex]
Factor out the GCF in each quantity
[tex](4x^2+5x)+(8x+10)\\x(4x+5)+2(4x+5)[/tex]
Now group x+2 together
[tex](x+2)(4x+5)[/tex]
Finally, set each factor equal to 0 and solve for x
[tex]x+2=0\\x+2-2=0-2\\x=-2\\\\\\4x+5=0\\4x+5-5=0-5\\4x=-5\\\frac{4x}{4} =\frac{-5}{4} \\x=-\frac{5}{4}[/tex]
