Solve for x (complex solution)
x\in \mathrm{C}
Solve for x
x\in \mathrm{R}
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5\left(x-4\right)-3\left(2x+5\right)=-\left(x+5\right)-30
Multiply both sides of the equation by 15, the least common multiple of 3,5,15.
5x-20-3\left(2x+5\right)=-\left(x+5\right)-30
Use the distributive property to multiply 5 by x-4.
5x-20-6x-15=-\left(x+5\right)-30
Use the distributive property to multiply -3 by 2x+5.
-x-20-15=-\left(x+5\right)-30
Combine 5x and -6x to get -x.
-x-35=-\left(x+5\right)-30
Subtract 15 from -20 to get -35.
-x-35=-x-5-30
To find the opposite of x+5, find the opposite of each term.
-x-35=-x-35
Subtract 30 from -5 to get -35.
-x-35+x=-35
Add x to both sides.
-35=-35
Combine -x and x to get 0.
\text{true}
Compare -35 and -35.
x\in \mathrm{C}
This is true for any x.
5\left(x-4\right)-3\left(2x+5\right)=-\left(x+5\right)-30
Multiply both sides of the equation by 15, the least common multiple of 3,5,15.
5x-20-3\left(2x+5\right)=-\left(x+5\right)-30
Use the distributive property to multiply 5 by x-4.
5x-20-6x-15=-\left(x+5\right)-30
Use the distributive property to multiply -3 by 2x+5.
-x-20-15=-\left(x+5\right)-30
Combine 5x and -6x to get -x.
-x-35=-\left(x+5\right)-30
Subtract 15 from -20 to get -35.
-x-35=-x-5-30
To find the opposite of x+5, find the opposite of each term.
-x-35=-x-35
Subtract 30 from -5 to get -35.
-x-35+x=-35
Add x to both sides.
-35=-35
Combine -x and x to get 0.
\text{true}
Compare -35 and -35.
x\in \mathrm{R}
This is true for any x.
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}