Solve for d (complex solution)
d\in \mathrm{C}
Solve for d
d\in \mathrm{R}
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12d-27=6\left(2d-5\right)+3
Use the distributive property to multiply 3 by 4d-9.
12d-27=12d-30+3
Use the distributive property to multiply 6 by 2d-5.
12d-27=12d-27
Add -30 and 3 to get -27.
12d-27-12d=-27
Subtract 12d from both sides.
-27=-27
Combine 12d and -12d to get 0.
\text{true}
Compare -27 and -27.
d\in \mathrm{C}
This is true for any d.
12d-27=6\left(2d-5\right)+3
Use the distributive property to multiply 3 by 4d-9.
12d-27=12d-30+3
Use the distributive property to multiply 6 by 2d-5.
12d-27=12d-27
Add -30 and 3 to get -27.
12d-27-12d=-27
Subtract 12d from both sides.
-27=-27
Combine 12d and -12d to get 0.
\text{true}
Compare -27 and -27.
d\in \mathrm{R}
This is true for any d.
Examples
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{ 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}