4t2+5=9t

Subtract 9t from both sides of the equation.

4t2+5-9t=0

Reorder terms.

4t2-9t+5=0

For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=4⋅5=20 and whose sum is b=-9.

Factor -9 out of -9t.

4t2-9t+5=0

Rewrite -9 as -4 plus -5

4t2+(-4-5)t+5=0

Apply the distributive property.

4t2-4t-5t+5=0

4t2-4t-5t+5=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(4t2-4t)-5t+5=0

Factor out the greatest common factor (GCF) from each group.

4t(t-1)-5(t-1)=0

4t(t-1)-5(t-1)=0

Factor the polynomial by factoring out the greatest common factor, t-1.

(t-1)(4t-5)=0

(t-1)(4t-5)=0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

t-1=0

4t-5=0

Set the first factor equal to 0.

t-1=0

Add 1 to both sides of the equation.

t=1

t=1

Set the next factor equal to 0.

4t-5=0

Add 5 to both sides of the equation.

4t=5

Divide each term by 4 and simplify.

Divide each term in 4t=5 by 4.

4t4=54

Cancel the common factor of 4.

Cancel the common factor.

4t4=54

Divide t by 1.

t=54

t=54

t=54

t=54

The final solution is all the values that make (t-1)(4t-5)=0 true.

t=1,54

The result can be shown in multiple forms.

Exact Form:

t=1,54

Decimal Form:

t=1,1.25

Mixed Number Form:

t=1,114

Solve for t 4t^2+5=9t