# Solve for t 4t^2+5=9t 4t2+5=9t
Subtract 9t from both sides of the equation.
4t2+5-9t=0
Factor by grouping.
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 and solve.
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 and solve.
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

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