Solve for x (complex solution)
x\in \mathrm{C}
Solve for x
x\in \mathrm{R}
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30\left(x-2\right)-15\left(5x-4\right)=-45x
Multiply both sides of the equation by 90, the least common multiple of 3,6,90.
30x-60-15\left(5x-4\right)=-45x
Use the distributive property to multiply 30 by x-2.
30x-60-75x+60=-45x
Use the distributive property to multiply -15 by 5x-4.
-45x-60+60=-45x
Combine 30x and -75x to get -45x.
-45x=-45x
Add -60 and 60 to get 0.
-45x+45x=0
Add 45x to both sides.
0=0
Combine -45x and 45x to get 0.
\text{true}
Compare 0 and 0.
x\in \mathrm{C}
This is true for any x.
30\left(x-2\right)-15\left(5x-4\right)=-45x
Multiply both sides of the equation by 90, the least common multiple of 3,6,90.
30x-60-15\left(5x-4\right)=-45x
Use the distributive property to multiply 30 by x-2.
30x-60-75x+60=-45x
Use the distributive property to multiply -15 by 5x-4.
-45x-60+60=-45x
Combine 30x and -75x to get -45x.
-45x=-45x
Add -60 and 60 to get 0.
-45x+45x=0
Add 45x to both sides.
0=0
Combine -45x and 45x to get 0.
\text{true}
Compare 0 and 0.
x\in \mathrm{R}
This is true for any x.
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}