Solve by Factoring 24x^6-18x^5=6x^5(4x-3)

$24 x^{6} - 18 x^{5} = 6 x^{5} (4 x - 3)$

Step 1

Subtract $6 x^{5} (4 x - 3)$ from both sides of the equation.

$24 x^{6} - 18 x^{5} - 6 x^{5} (4 x - 3) = 0$

Step 2

Simplify $24 x^{6} - 18 x^{5} - 6 x^{5} (4 x - 3)$ .

Simplify each term.

Apply the distributive property.

$24 x^{6} - 18 x^{5} - 6 x^{5} (4 x) - 6 x^{5} \cdot - 3 = 0$

Rewrite using the commutative property of multiplication.

$24 x^{6} - 18 x^{5} - 6 \cdot 4 x^{5} x - 6 x^{5} \cdot - 3 = 0$

Multiply $- 3$ by $- 6$ .

$24 x^{6} - 18 x^{5} - 6 \cdot 4 x^{5} x + 18 x^{5} = 0$

Simplify each term.

Multiply $x^{5}$ by $x$ by adding the exponents.

Move $x$ .

$24 x^{6} - 18 x^{5} - 6 \cdot 4 (x \cdot x^{5}) + 18 x^{5} = 0$

Multiply $x$ by $x^{5}$ .

Raise $x$ to the power of $1$ .

$24 x^{6} - 18 x^{5} - 6 \cdot 4 (x^{1} x^{5}) + 18 x^{5} = 0$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$24 x^{6} - 18 x^{5} - 6 \cdot 4 x^{1 + 5} + 18 x^{5} = 0$

Add $1$ and $5$ .

$24 x^{6} - 18 x^{5} - 6 \cdot 4 x^{6} + 18 x^{5} = 0$

Multiply $- 6$ by $4$ .

$24 x^{6} - 18 x^{5} - 24 x^{6} + 18 x^{5} = 0$

Combine the opposite terms in $24 x^{6} - 18 x^{5} - 24 x^{6} + 18 x^{5}$ .

Subtract $24 x^{6}$ from $24 x^{6}$ .

$- 18 x^{5} + 0 + 18 x^{5} = 0$

Add $- 18 x^{5}$ and $0$ .

$- 18 x^{5} + 18 x^{5} = 0$

Add $- 18 x^{5}$ and $18 x^{5}$ .

$0 = 0$

Step 3

Since $0 = 0$ , the equation will always be true.

Always true