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Question
4m^{2}-15m+5=-3m
Solve the quadratic equation
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Solve by factoring
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Solve using the quadratic formula
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Solve by completing the square
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Solve using the PQ formula
More methods
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m_{1}=\frac{1}{2},m_{2}=\frac{5}{2}
Alternative Form
m_{1}=0.5,m_{2}=2.5
Evaluate
4m^{2}-15m+5=-3m
Move the expression to the left side
4m^{2}-12m+5=0
Factor the expression
More Steps
Evaluate
4m^{2}-12m+5
Rewrite the expression
4m^{2}+\left(-2-10\right)m+5
Calculate
4m^{2}-2m-10m+5
Rewrite the expression
2m\times 2m-2m-5\times 2m+5
\text{Factor out }2m\text{ from the expression}
2m\left(2m-1\right)-5\times 2m+5
\text{Factor out }-5\text{ from the expression}
2m\left(2m-1\right)-5\left(2m-1\right)
\text{Factor out }2m-1\text{ from the expression}
\left(2m-5\right)\left(2m-1\right)
\left(2m-5\right)\left(2m-1\right)=0
When the product of factors equals 0,at least one factor is 0
\begin{align}&2m-5=0\\&2m-1=0\end{align}
\text{Solve the equation for }m
More Steps
Evaluate
2m-5=0
Move the constant to the right-hand side and change its sign
2m=0+5
Removing 0 doesn't change the value,so remove it from the expression
2m=5
Divide both sides
\frac{2m}{2}=\frac{5}{2}
Divide the numbers
m=\frac{5}{2}
\begin{align}&m=\frac{5}{2}\\&2m-1=0\end{align}
\text{Solve the equation for }m
More Steps
Evaluate
2m-1=0
Move the constant to the right-hand side and change its sign
2m=0+1
Removing 0 doesn't change the value,so remove it from the expression
2m=1
Divide both sides
\frac{2m}{2}=\frac{1}{2}
Divide the numbers
m=\frac{1}{2}
\begin{align}&m=\frac{5}{2}\\&m=\frac{1}{2}\end{align}
Solution
m_{1}=\frac{1}{2},m_{2}=\frac{5}{2}
Alternative Form
m_{1}=0.5,m_{2}=2.5
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