Evaluate
-\frac{3x^{2}}{2}+\frac{19x}{2}-12
Expand
-\frac{3x^{2}}{2}+\frac{19x}{2}-12
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\frac{2}{2}+2\left(x-2\right)-\frac{3\left(x-2\right)\left(x-3\right)}{2}
To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{2}{2}.
\frac{2-3\left(x-2\right)\left(x-3\right)}{2}+2\left(x-2\right)
Since \frac{2}{2} and \frac{3\left(x-2\right)\left(x-3\right)}{2} have the same denominator, subtract them by subtracting their numerators.
\frac{2-3x^{2}+9x+6x-18}{2}+2\left(x-2\right)
Do the multiplications in 2-3\left(x-2\right)\left(x-3\right).
\frac{-16-3x^{2}+15x}{2}+2\left(x-2\right)
Combine like terms in 2-3x^{2}+9x+6x-18.
1+2x-4-\frac{3\left(x-2\right)\left(x-3\right)}{2}
Use the distributive property to multiply 2 by x-2.
-3+2x-\frac{3\left(x-2\right)\left(x-3\right)}{2}
Subtract 4 from 1 to get -3.
-3+2x-\frac{\left(3x-6\right)\left(x-3\right)}{2}
Use the distributive property to multiply 3 by x-2.
-3+2x-\frac{3x^{2}-9x-6x+18}{2}
Apply the distributive property by multiplying each term of 3x-6 by each term of x-3.
-3+2x-\frac{3x^{2}-15x+18}{2}
Combine -9x and -6x to get -15x.
\frac{2\left(-3+2x\right)}{2}-\frac{3x^{2}-15x+18}{2}
To add or subtract expressions, expand them to make their denominators the same. Multiply -3+2x times \frac{2}{2}.
\frac{2\left(-3+2x\right)-\left(3x^{2}-15x+18\right)}{2}
Since \frac{2\left(-3+2x\right)}{2} and \frac{3x^{2}-15x+18}{2} have the same denominator, subtract them by subtracting their numerators.
\frac{-6+4x-3x^{2}+15x-18}{2}
Do the multiplications in 2\left(-3+2x\right)-\left(3x^{2}-15x+18\right).
\frac{-24+19x-3x^{2}}{2}
Combine like terms in -6+4x-3x^{2}+15x-18.
\frac{2}{2}+2\left(x-2\right)-\frac{3\left(x-2\right)\left(x-3\right)}{2}
To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{2}{2}.
\frac{2-3\left(x-2\right)\left(x-3\right)}{2}+2\left(x-2\right)
Since \frac{2}{2} and \frac{3\left(x-2\right)\left(x-3\right)}{2} have the same denominator, subtract them by subtracting their numerators.
\frac{2-3x^{2}+9x+6x-18}{2}+2\left(x-2\right)
Do the multiplications in 2-3\left(x-2\right)\left(x-3\right).
\frac{-16-3x^{2}+15x}{2}+2\left(x-2\right)
Combine like terms in 2-3x^{2}+9x+6x-18.
1+2x-4-\frac{3\left(x-2\right)\left(x-3\right)}{2}
Use the distributive property to multiply 2 by x-2.
-3+2x-\frac{3\left(x-2\right)\left(x-3\right)}{2}
Subtract 4 from 1 to get -3.
-3+2x-\frac{\left(3x-6\right)\left(x-3\right)}{2}
Use the distributive property to multiply 3 by x-2.
-3+2x-\frac{3x^{2}-9x-6x+18}{2}
Apply the distributive property by multiplying each term of 3x-6 by each term of x-3.
-3+2x-\frac{3x^{2}-15x+18}{2}
Combine -9x and -6x to get -15x.
\frac{2\left(-3+2x\right)}{2}-\frac{3x^{2}-15x+18}{2}
To add or subtract expressions, expand them to make their denominators the same. Multiply -3+2x times \frac{2}{2}.
\frac{2\left(-3+2x\right)-\left(3x^{2}-15x+18\right)}{2}
Since \frac{2\left(-3+2x\right)}{2} and \frac{3x^{2}-15x+18}{2} have the same denominator, subtract them by subtracting their numerators.
\frac{-6+4x-3x^{2}+15x-18}{2}
Do the multiplications in 2\left(-3+2x\right)-\left(3x^{2}-15x+18\right).
\frac{-24+19x-3x^{2}}{2}
Combine like terms in -6+4x-3x^{2}+15x-18.
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}