Basic Math Examples

$d^{2} c a = b^{4} c^{3} a^{2}$

Step 1

Subtract $b^{4} c^{3} a^{2}$ from both sides of the equation.

$d^{2} c a - b^{4} c^{3} a^{2} = 0$

Step 2

Factor $c a$ out of $d^{2} c a - b^{4} c^{3} a^{2}$ .

Tap for more steps...

Step 2.1

Factor $c a$ out of $d^{2} c a$ .

$c a (d^{2}) - b^{4} c^{3} a^{2} = 0$

Step 2.2

Factor $c a$ out of $- b^{4} c^{3} a^{2}$ .

$c a (d^{2}) + c a (- b^{4} c^{2} a) = 0$

Step 2.3

Factor $c a$ out of $c a (d^{2}) + c a (- b^{4} c^{2} a)$ .

$c a (d^{2} - b^{4} c^{2} a) = 0$

Step 3

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$a = 0$

$d^{2} - b^{4} c^{2} a = 0$

Step 4

Set $a$ equal to $0$ .

$a = 0$

Step 5

Set $d^{2} - b^{4} c^{2} a$ equal to $0$ and solve for $a$ .

Tap for more steps...

Step 5.1

Set $d^{2} - b^{4} c^{2} a$ equal to $0$ .

$d^{2} - b^{4} c^{2} a = 0$

Step 5.2

Solve $d^{2} - b^{4} c^{2} a = 0$ for $a$ .

Tap for more steps...

Step 5.2.1

Subtract $d^{2}$ from both sides of the equation.

$- b^{4} c^{2} a = - d^{2}$

Step 5.2.2

Divide each term in $- b^{4} c^{2} a = - d^{2}$ by $- b^{4} c^{2}$ and simplify.

Tap for more steps...

Step 5.2.2.1

Divide each term in $- b^{4} c^{2} a = - d^{2}$ by $- b^{4} c^{2}$ .

$\frac{- b^{4} c^{2} a}{- b^{4} c^{2}} = \frac{- d^{2}}{- b^{4} c^{2}}$

Step 5.2.2.2

Simplify the left side.

Tap for more steps...

Step 5.2.2.2.1

Dividing two negative values results in a positive value.

$\frac{b^{4} c^{2} a}{b^{4} c^{2}} = \frac{- d^{2}}{- b^{4} c^{2}}$

Step 5.2.2.2.2

Cancel the common factor of $b^{4}$ .

Tap for more steps...

Step 5.2.2.2.2.1

Cancel the common factor.

$\frac{b^{4} c^{2} a}{b^{4} c^{2}} = \frac{- d^{2}}{- b^{4} c^{2}}$

Step 5.2.2.2.2.2

Rewrite the expression.

$\frac{c^{2} a}{c^{2}} = \frac{- d^{2}}{- b^{4} c^{2}}$

Step 5.2.2.2.3

Cancel the common factor of $c^{2}$ .

Tap for more steps...

Step 5.2.2.2.3.1

Cancel the common factor.

$\frac{c^{2} a}{c^{2}} = \frac{- d^{2}}{- b^{4} c^{2}}$

Step 5.2.2.2.3.2

Divide $a$ by $1$ .

$a = \frac{- d^{2}}{- b^{4} c^{2}}$

Step 5.2.2.3

Simplify the right side.

Tap for more steps...

Step 5.2.2.3.1

Dividing two negative values results in a positive value.

$a = \frac{d^{2}}{b^{4} c^{2}}$

Step 6

The final solution is all the values that make $c a (d^{2} - b^{4} c^{2} a) = 0$ true.

$a = 0$

$a = \frac{d^{2}}{b^{4} c^{2}}$