Questions: Solve. (x-3)(x+6)=10 x x=

Solution Steps

To solve the equation \((x-3)(x+6)=10x\), we first expand the left-hand side and then bring all terms to one side of the equation to form a quadratic equation. Next, we solve the quadratic equation using the quadratic formula or by factoring, if possible.

We start with the equation: \[ (x - 3)(x + 6) = 10x \] Expanding the left-hand side gives: \[ x^2 + 6x - 3x - 18 = 10x \] which simplifies to: \[ x^2 + 3x - 18 = 10x \]

Next, we rearrange the equation by moving all terms to one side: \[ x^2 + 3x - 10x - 18 = 0 \] This simplifies to: \[ x^2 - 7x - 18 = 0 \]

We can solve the quadratic equation \(x^2 - 7x - 18 = 0\) using the quadratic formula: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] where \(a = 1\), \(b = -7\), and \(c = -18\). This yields the solutions: \[ x = -2 \quad \text{and} \quad x = 9 \]

Final Answer