"subtract 10 from both sides"subtract 10 from both sides
y^2+3/2y-10=0y2+32y−10=0
"multiply through by 2"multiply through by 2
2y^2+3y-20=02y2+3y−20=0
"factor the quadratic using the a-c method"factor the quadratic using the a-c method
"the factors of the product "2xx-20=-40the factors of the product 2×−20=−40
"which sum to "+3" are "+8" and "-5which sum to +3 are +8 and −5
"split the middle term using these factors"split the middle term using these factors
2y^2+8y-5y-20=0larrcolor(blue)"factor by grouping"2y2+8y−5y−20=0←factor by grouping
color(red)(2y)(y+4)color(red)(-5)(y+4)=02y(y+4)−5(y+4)=0
"take out the "color(blue)"common factor "(y+4)take out the common factor (y+4)
(y+4)(color(red)(2y-5))=0(y+4)(2y−5)=0
"equate each factor to zero and solve for y"equate each factor to zero and solve for y
y+4=0rArry=-4y+4=0⇒y=−4
2y-5=0rArry=5/22y−5=0⇒y=52