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Question
20x^{2}+3x-9
Factor the expression
\left(4x+3\right)\left(5x-3\right)
Evaluate
20x^{2}+3x-9
Rewrite the expression
20x^{2}+\left(-12+15\right)x-9
Calculate
20x^{2}-12x+15x-9
Rewrite the expression
4x\times 5x-4x\times 3+3\times 5x-3\times 3
\text{Factor out }4x\text{ from the expression}
4x\left(5x-3\right)+3\times 5x-3\times 3
\text{Factor out }3\text{ from the expression}
4x\left(5x-3\right)+3\left(5x-3\right)
Solution
\left(4x+3\right)\left(5x-3\right)
Show Solutions
Find the roots
x_{1}=-\frac{3}{4},x_{2}=\frac{3}{5}
Alternative Form
x_{1}=-0.75,x_{2}=0.6
Evaluate
20x^{2}+3x-9
To find the roots of the expression,set the expression equal to 0
20x^{2}+3x-9=0
Factor the expression
More Steps
Evaluate
20x^{2}+3x-9
Rewrite the expression
20x^{2}+\left(-12+15\right)x-9
Calculate
20x^{2}-12x+15x-9
Rewrite the expression
4x\times 5x-4x\times 3+3\times 5x-3\times 3
\text{Factor out }4x\text{ from the expression}
4x\left(5x-3\right)+3\times 5x-3\times 3
\text{Factor out }3\text{ from the expression}
4x\left(5x-3\right)+3\left(5x-3\right)
\text{Factor out }5x-3\text{ from the expression}
\left(4x+3\right)\left(5x-3\right)
\left(4x+3\right)\left(5x-3\right)=0
When the product of factors equals 0,at least one factor is 0
\begin{align}&4x+3=0\\&5x-3=0\end{align}
\text{Solve the equation for }x
More Steps
Evaluate
4x+3=0
Move the constant to the right-hand side and change its sign
4x=0-3
Removing 0 doesn't change the value,so remove it from the expression
4x=-3
Divide both sides
\frac{4x}{4}=\frac{-3}{4}
Divide the numbers
x=\frac{-3}{4}
\text{Use }\frac{-a}{b}=\frac{a}{-b}=-\frac{a}{b}\text{ to rewrite the fraction}
x=-\frac{3}{4}
\begin{align}&x=-\frac{3}{4}\\&5x-3=0\end{align}
\text{Solve the equation for }x
More Steps
Evaluate
5x-3=0
Move the constant to the right-hand side and change its sign
5x=0+3
Removing 0 doesn't change the value,so remove it from the expression
5x=3
Divide both sides
\frac{5x}{5}=\frac{3}{5}
Divide the numbers
x=\frac{3}{5}
\begin{align}&x=-\frac{3}{4}\\&x=\frac{3}{5}\end{align}
Solution
x_{1}=-\frac{3}{4},x_{2}=\frac{3}{5}
Alternative Form
x_{1}=-0.75,x_{2}=0.6
Show Solutions
