Evaluate
-\frac{\left(x-4\right)\left(3x+2\right)}{2}
Expand
-\frac{3x^{2}}{2}+5x+4
Graph
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\left(-\frac{1}{2}x-\frac{1}{2}\left(-4\right)\right)\left(3x+2\right)
Use the distributive property to multiply -\frac{1}{2} by x-4.
\left(-\frac{1}{2}x+\frac{-\left(-4\right)}{2}\right)\left(3x+2\right)
Express -\frac{1}{2}\left(-4\right) as a single fraction.
\left(-\frac{1}{2}x+\frac{4}{2}\right)\left(3x+2\right)
Multiply -1 and -4 to get 4.
\left(-\frac{1}{2}x+2\right)\left(3x+2\right)
Divide 4 by 2 to get 2.
-\frac{1}{2}x\times 3x-\frac{1}{2}x\times 2+6x+4
Apply the distributive property by multiplying each term of -\frac{1}{2}x+2 by each term of 3x+2.
-\frac{1}{2}x^{2}\times 3-\frac{1}{2}x\times 2+6x+4
Multiply x and x to get x^{2}.
\frac{-3}{2}x^{2}-\frac{1}{2}x\times 2+6x+4
Express -\frac{1}{2}\times 3 as a single fraction.
-\frac{3}{2}x^{2}-\frac{1}{2}x\times 2+6x+4
Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.
-\frac{3}{2}x^{2}-x+6x+4
Cancel out 2 and 2.
-\frac{3}{2}x^{2}+5x+4
Combine -x and 6x to get 5x.
\left(-\frac{1}{2}x-\frac{1}{2}\left(-4\right)\right)\left(3x+2\right)
Use the distributive property to multiply -\frac{1}{2} by x-4.
\left(-\frac{1}{2}x+\frac{-\left(-4\right)}{2}\right)\left(3x+2\right)
Express -\frac{1}{2}\left(-4\right) as a single fraction.
\left(-\frac{1}{2}x+\frac{4}{2}\right)\left(3x+2\right)
Multiply -1 and -4 to get 4.
\left(-\frac{1}{2}x+2\right)\left(3x+2\right)
Divide 4 by 2 to get 2.
-\frac{1}{2}x\times 3x-\frac{1}{2}x\times 2+6x+4
Apply the distributive property by multiplying each term of -\frac{1}{2}x+2 by each term of 3x+2.
-\frac{1}{2}x^{2}\times 3-\frac{1}{2}x\times 2+6x+4
Multiply x and x to get x^{2}.
\frac{-3}{2}x^{2}-\frac{1}{2}x\times 2+6x+4
Express -\frac{1}{2}\times 3 as a single fraction.
-\frac{3}{2}x^{2}-\frac{1}{2}x\times 2+6x+4
Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.
-\frac{3}{2}x^{2}-x+6x+4
Cancel out 2 and 2.
-\frac{3}{2}x^{2}+5x+4
Combine -x and 6x to get 5x.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}