Solve for x
x=0
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\frac{2x}{5}=\frac{3x}{2+6}
Add 3 and 2 to get 5.
\frac{2x}{5}=\frac{3x}{8}
Add 2 and 6 to get 8.
\frac{2x}{5}-\frac{3x}{8}=0
Subtract \frac{3x}{8} from both sides.
\frac{8\times 2x}{40}-\frac{5\times 3x}{40}=0
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 8 is 40. Multiply \frac{2x}{5} times \frac{8}{8}. Multiply \frac{3x}{8} times \frac{5}{5}.
\frac{8\times 2x-5\times 3x}{40}=0
Since \frac{8\times 2x}{40} and \frac{5\times 3x}{40} have the same denominator, subtract them by subtracting their numerators.
\frac{16x-15x}{40}=0
Do the multiplications in 8\times 2x-5\times 3x.
\frac{x}{40}=0
Combine like terms in 16x-15x.
x=0
Multiply both sides by 40. Anything times zero gives zero.
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}