Solve for x 3x(x-1)=(3x-3)(x+5)

$3 x (x - 1) = (3 x - 3) (x + 5)$

Step 1

Simplify $3 x (x - 1)$ .

Start simplifying.

$0 + 0 + 3 x (x - 1) = (3 x - 3) (x + 5)$

Simplify by adding zeros.

$3 x (x - 1) = (3 x - 3) (x + 5)$

Apply the distributive property.

$3 x \cdot x + 3 x \cdot - 1 = (3 x - 3) (x + 5)$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$3 (x \cdot x) + 3 x \cdot - 1 = (3 x - 3) (x + 5)$

Multiply $x$ by $x$ .

$3 x^{2} + 3 x \cdot - 1 = (3 x - 3) (x + 5)$

Multiply $- 1$ by $3$ .

$3 x^{2} - 3 x = (3 x - 3) (x + 5)$

Step 2

Simplify $(3 x - 3) (x + 5)$ .

Expand $(3 x - 3) (x + 5)$ using the FOIL Method.

Apply the distributive property.

$3 x^{2} - 3 x = 3 x (x + 5) - 3 (x + 5)$

Apply the distributive property.

$3 x^{2} - 3 x = 3 x \cdot x + 3 x \cdot 5 - 3 (x + 5)$

Apply the distributive property.

$3 x^{2} - 3 x = 3 x \cdot x + 3 x \cdot 5 - 3 x - 3 \cdot 5$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$3 x^{2} - 3 x = 3 (x \cdot x) + 3 x \cdot 5 - 3 x - 3 \cdot 5$

Multiply $x$ by $x$ .

$3 x^{2} - 3 x = 3 x^{2} + 3 x \cdot 5 - 3 x - 3 \cdot 5$

Multiply $5$ by $3$ .

$3 x^{2} - 3 x = 3 x^{2} + 15 x - 3 x - 3 \cdot 5$

Multiply $- 3$ by $5$ .

$3 x^{2} - 3 x = 3 x^{2} + 15 x - 3 x - 15$

Subtract $3 x$ from $15 x$ .

$3 x^{2} - 3 x = 3 x^{2} + 12 x - 15$

Step 3

Move all terms containing $x$ to the left side of the equation.

Subtract $3 x^{2}$ from both sides of the equation.

$3 x^{2} - 3 x - 3 x^{2} = 12 x - 15$

Subtract $12 x$ from both sides of the equation.

$3 x^{2} - 3 x - 3 x^{2} - 12 x = - 15$

Combine the opposite terms in $3 x^{2} - 3 x - 3 x^{2} - 12 x$ .

Subtract $3 x^{2}$ from $3 x^{2}$ .

$- 3 x + 0 - 12 x = - 15$

Add $- 3 x$ and $0$ .

$- 3 x - 12 x = - 15$

Subtract $12 x$ from $- 3 x$ .

$- 15 x = - 15$

Step 4

Divide each term in $- 15 x = - 15$ by $- 15$ and simplify.

Divide each term in $- 15 x = - 15$ by $- 15$ .

$\frac{- 15 x}{- 15} = \frac{- 15}{- 15}$

Simplify the left side.

Cancel the common factor of $- 15$ .

Cancel the common factor.

$\frac{- 15 x}{- 15} = \frac{- 15}{- 15}$

Divide $x$ by $1$ .

$x = \frac{- 15}{- 15}$

Simplify the right side.

Divide $- 15$ by $- 15$ .

$x = 1$

Solve for x 3x(x-1)=(3x-3)(x+5)

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