Solve the equation. $$ x(3 x-9)=(3 x+5)(x-7) $$

Question

UpStudy AI · Accepted Answer

We start with the equation
$$
x(3x-9) = (3x+5)(x-7).
$$

**Step 1. Expand both sides.**

For the left-hand side:
$$
x(3x-9) = 3x^2 - 9x.
$$

For the right-hand side:
$$
(3x+5)(x-7) = 3x\cdot x + 3x\cdot(-7) + 5\cdot x + 5\cdot(-7) = 3x^2 - 21x + 5x - 35 = 3x^2 - 16x - 35.
$$

**Step 2. Set the expanded equations equal to each other.**

$$
3x^2 - 9x = 3x^2 - 16x - 35.
$$

**Step 3. Eliminate the quadratic term.**

Subtract $$3x^2$$ from both sides:
$$
-9x = -16x - 35.
$$

**Step 4. Solve for $$ x $$.**

Add $$16x$$ to both sides:
$$
7x = -35.
$$

Divide both sides by $$7$$:
$$
x = -5.
$$

The solution to the equation is:
$$
x = -5.
$$
$$ x = -5 $$

Solve the equation.