Solve for a
a=0
b\neq -5
Solve for b
b\neq -5
a=0\text{ and }b\neq -5
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3a\left(b+5\right)=4\times 0
Multiply both sides of the equation by b+5.
3ab+15a=4\times 0
Use the distributive property to multiply 3a by b+5.
3ab+15a=0
Multiply 4 and 0 to get 0.
\left(3b+15\right)a=0
Combine all terms containing a.
a=0
Divide 0 by 3b+15.
3a\left(b+5\right)=4\times 0
Variable b cannot be equal to -5 since division by zero is not defined. Multiply both sides of the equation by b+5.
3ab+15a=4\times 0
Use the distributive property to multiply 3a by b+5.
3ab+15a=0
Multiply 4 and 0 to get 0.
3ab=-15a
Subtract 15a from both sides. Anything subtracted from zero gives its negation.
\frac{3ab}{3a}=-\frac{15a}{3a}
Divide both sides by 3a.
b=-\frac{15a}{3a}
Dividing by 3a undoes the multiplication by 3a.
b=-5
Divide -15a by 3a.
b\in \emptyset
Variable b cannot be equal to -5.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
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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}