Question
Factor the expression
(t−2)(3t+1)
Evaluate
3t2−5t−2
Rewrite the expression
3t2+(1−6)t−2
Calculate
3t2+t−6t−2
Rewrite the expression
t×3t+t−2×3t−2
Factor out t from the expression
t(3t+1)−2×3t−2
Factor out −2 from the expression
t(3t+1)−2(3t+1)
Solution
(t−2)(3t+1)
Show Solution

Find the roots
t1=−31,t2=2
Alternative Form
t1=−0.3˙,t2=2
Evaluate
3t2−5t−2
To find the roots of the expression,set the expression equal to 0
3t2−5t−2=0
Factor the expression
More Steps

Evaluate
3t2−5t−2
Rewrite the expression
3t2+(1−6)t−2
Calculate
3t2+t−6t−2
Rewrite the expression
t×3t+t−2×3t−2
Factor out t from the expression
t(3t+1)−2×3t−2
Factor out −2 from the expression
t(3t+1)−2(3t+1)
Factor out 3t+1 from the expression
(t−2)(3t+1)
(t−2)(3t+1)=0
When the product of factors equals 0,at least one factor is 0
t−2=03t+1=0
Solve the equation for t
More Steps

Evaluate
t−2=0
Move the constant to the right-hand side and change its sign
t=0+2
Removing 0 doesn't change the value,so remove it from the expression
t=2
t=23t+1=0
Solve the equation for t
More Steps

Evaluate
3t+1=0
Move the constant to the right-hand side and change its sign
3t=0−1
Removing 0 doesn't change the value,so remove it from the expression
3t=−1
Divide both sides
33t=3−1
Divide the numbers
t=3−1
Use b−a=−ba=−ba to rewrite the fraction
t=−31
t=2t=−31
Solution
t1=−31,t2=2
Alternative Form
t1=−0.3˙,t2=2
Show Solution
