Solve -y^2/a+7x/b-18/c=0

$$- \frac { y ^ { 2 } } { a } + \frac { 7 x } { b } - \frac { 18 } { c } = 0$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{bcy^{2}}{18b-7cx}\text{, }&c\neq 0\text{ and }b\neq 0\text{ and }y\neq 0\text{ and }b\neq \frac{7cx}{18}\\a\neq 0\text{, }&b=\frac{7cx}{18}\text{ and }y=0\text{ and }c\neq 0\text{ and }x\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by abc, the least common multiple of a,b,c.

$$-bcy^{2}+ac\times 7x-ab\times 18=0$$

Add bcy^{2} to both sides. Anything plus zero gives itself.

$$ac\times 7x-ab\times 18=bcy^{2}$$

Multiply -1 and 18 to get -18.

$$ac\times 7x-18ab=bcy^{2}$$

Combine all terms containing a.

$$\left(c\times 7x-18b\right)a=bcy^{2}$$

The equation is in standard form.

$$\left(7cx-18b\right)a=bcy^{2}$$

Divide both sides by 7xc-18b.

$$\frac{\left(7cx-18b\right)a}{7cx-18b}=\frac{bcy^{2}}{7cx-18b}$$

Dividing by 7xc-18b undoes the multiplication by 7xc-18b.

$$a=\frac{bcy^{2}}{7cx-18b}$$

Variable a cannot be equal to 0.

$$a=\frac{bcy^{2}}{7cx-18b}\text{, }a\neq 0$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=\frac{7acx}{cy^{2}+18a}\text{, }&c\neq 0\text{ and }a\neq 0\text{ and }x\neq 0\text{ and }a\neq -\frac{cy^{2}}{18}\text{ and }y\neq -3ic^{-\frac{1}{2}}\sqrt{2a}\text{ and }y\neq 3ic^{-\frac{1}{2}}\sqrt{2a}\\b\neq 0\text{, }&a=-\frac{cy^{2}}{18}\text{ and }x=0\text{ and }c\neq 0\text{ and }y\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable b cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by abc, the least common multiple of a,b,c.

$$-bcy^{2}+ac\times 7x-ab\times 18=0$$

Subtract ac\times 7x from both sides. Anything subtracted from zero gives its negation.

$$-bcy^{2}-ab\times 18=-ac\times 7x$$

Multiply -1 and 18 to get -18.

$$-bcy^{2}-18ab=-ac\times 7x$$

Multiply -1 and 7 to get -7.

$$-bcy^{2}-18ab=-7acx$$

Combine all terms containing b.

$$\left(-cy^{2}-18a\right)b=-7acx$$

Divide both sides by -y^{2}c-18a.

$$\frac{\left(-cy^{2}-18a\right)b}{-cy^{2}-18a}=-\frac{7acx}{-cy^{2}-18a}$$

Dividing by -y^{2}c-18a undoes the multiplication by -y^{2}c-18a.

$$b=-\frac{7acx}{-cy^{2}-18a}$$

Divide -7acx by -y^{2}c-18a.

$$b=\frac{7acx}{cy^{2}+18a}$$

Variable b cannot be equal to 0.

$$b=\frac{7acx}{cy^{2}+18a}\text{, }b\neq 0$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{bcy^{2}}{18b-7cx}\text{, }&c\neq 0\text{ and }b\neq 0\text{ and }y\neq 0\text{ and }b\neq \frac{7cx}{18}\\a\neq 0\text{, }&b=\frac{7cx}{18}\text{ and }y=0\text{ and }x\neq 0\text{ and }c\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by abc, the least common multiple of a,b,c.

$$-bcy^{2}+ac\times 7x-ab\times 18=0$$

Add bcy^{2} to both sides. Anything plus zero gives itself.

$$ac\times 7x-ab\times 18=bcy^{2}$$

Multiply -1 and 18 to get -18.

$$ac\times 7x-18ab=bcy^{2}$$

Combine all terms containing a.

$$\left(c\times 7x-18b\right)a=bcy^{2}$$

The equation is in standard form.

$$\left(7cx-18b\right)a=bcy^{2}$$

Divide both sides by 7cx-18b.

$$\frac{\left(7cx-18b\right)a}{7cx-18b}=\frac{bcy^{2}}{7cx-18b}$$

Dividing by 7cx-18b undoes the multiplication by 7cx-18b.

$$a=\frac{bcy^{2}}{7cx-18b}$$

Variable a cannot be equal to 0.

$$a=\frac{bcy^{2}}{7cx-18b}\text{, }a\neq 0$$

Solve for b

$$\left\{\begin{matrix}b=\frac{7acx}{cy^{2}+18a}\text{, }&x\neq 0\text{ and }a\neq 0\text{ and }\left(a>0\text{ or }c<0\text{ or }|y|\neq 3\sqrt{-\frac{2a}{c}}\right)\text{ and }\left(c>0\text{ or }a<0\text{ or }|y|\neq 3\sqrt{-\frac{2a}{c}}\right)\text{ and }c\neq 0\text{ and }a\neq -\frac{cy^{2}}{18}\\b\neq 0\text{, }&a=-\frac{cy^{2}}{18}\text{ and }x=0\text{ and }c\neq 0\text{ and }y\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable b cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by abc, the least common multiple of a,b,c.

$$-bcy^{2}+ac\times 7x-ab\times 18=0$$

Subtract ac\times 7x from both sides. Anything subtracted from zero gives its negation.

$$-bcy^{2}-ab\times 18=-ac\times 7x$$

Multiply -1 and 18 to get -18.

$$-bcy^{2}-18ab=-ac\times 7x$$

Multiply -1 and 7 to get -7.

$$-bcy^{2}-18ab=-7acx$$

Combine all terms containing b.

$$\left(-cy^{2}-18a\right)b=-7acx$$

Divide both sides by -y^{2}c-18a.

$$\frac{\left(-cy^{2}-18a\right)b}{-cy^{2}-18a}=-\frac{7acx}{-cy^{2}-18a}$$

Dividing by -y^{2}c-18a undoes the multiplication by -y^{2}c-18a.

$$b=-\frac{7acx}{-cy^{2}-18a}$$

Divide -7acx by -y^{2}c-18a.

$$b=\frac{7acx}{cy^{2}+18a}$$

Variable b cannot be equal to 0.

$$b=\frac{7acx}{cy^{2}+18a}\text{, }b\neq 0$$