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Question
5t^{2}-24t-5
Factor the expression
\left(t-5\right)\left(5t+1\right)
Evaluate
5t^{2}-24t-5
Rewrite the expression
5t^{2}+\left(1-25\right)t-5
Calculate
5t^{2}+t-25t-5
Rewrite the expression
t\times 5t+t-5\times 5t-5
\text{Factor out }t\text{ from the expression}
t\left(5t+1\right)-5\times 5t-5
\text{Factor out }-5\text{ from the expression}
t\left(5t+1\right)-5\left(5t+1\right)
Solution
\left(t-5\right)\left(5t+1\right)
Show Solutions
Find the roots
t_{1}=-\frac{1}{5},t_{2}=5
Alternative Form
t_{1}=-0.2,t_{2}=5
Evaluate
5t^{2}-24t-5
To find the roots of the expression,set the expression equal to 0
5t^{2}-24t-5=0
Factor the expression
More Steps
Evaluate
5t^{2}-24t-5
Rewrite the expression
5t^{2}+\left(1-25\right)t-5
Calculate
5t^{2}+t-25t-5
Rewrite the expression
t\times 5t+t-5\times 5t-5
\text{Factor out }t\text{ from the expression}
t\left(5t+1\right)-5\times 5t-5
\text{Factor out }-5\text{ from the expression}
t\left(5t+1\right)-5\left(5t+1\right)
\text{Factor out }5t+1\text{ from the expression}
\left(t-5\right)\left(5t+1\right)
\left(t-5\right)\left(5t+1\right)=0
When the product of factors equals 0,at least one factor is 0
\begin{align}&t-5=0\\&5t+1=0\end{align}
\text{Solve the equation for }t
More Steps
Evaluate
t-5=0
Move the constant to the right-hand side and change its sign
t=0+5
Removing 0 doesn't change the value,so remove it from the expression
t=5
\begin{align}&t=5\\&5t+1=0\end{align}
\text{Solve the equation for }t
More Steps
Evaluate
5t+1=0
Move the constant to the right-hand side and change its sign
5t=0-1
Removing 0 doesn't change the value,so remove it from the expression
5t=-1
Divide both sides
\frac{5t}{5}=\frac{-1}{5}
Divide the numbers
t=\frac{-1}{5}
\text{Use }\frac{-a}{b}=\frac{a}{-b}=-\frac{a}{b}\text{ to rewrite the fraction}
t=-\frac{1}{5}
\begin{align}&t=5\\&t=-\frac{1}{5}\end{align}
Solution
t_{1}=-\frac{1}{5},t_{2}=5
Alternative Form
t_{1}=-0.2,t_{2}=5
Show Solutions
