Questions: Solve the equation by factoring. 8-8x=(3x+1)(x-1)

Solution Steps

To solve the equation by factoring, we first need to expand the right-hand side and then move all terms to one side of the equation to set it to zero. After that, we can factor the resulting quadratic equation and solve for \( x \).

First, we expand the right-hand side of the equation: \[ (3x + 1)(x - 1) = 3x^2 - 3x + x - 1 = 3x^2 - 2x - 1 \]

Next, we move all terms to one side of the equation to set it to zero: \[ 8 - 8x - (3x^2 - 2x - 1) = 0 \] Simplifying this, we get: \[ 8 - 8x - 3x^2 + 2x + 1 = 0 \] \[ -3x^2 - 6x + 9 = 0 \]

We factor the quadratic equation: \[ -3x^2 - 6x + 9 = 0 \] Factoring out \(-3\), we get: \[ -3(x^2 + 2x - 3) = 0 \] Solving \(x^2 + 2x - 3 = 0\), we factor it as: \[ (x + 3)(x - 1) = 0 \]

Setting each factor to zero, we solve for \( x \): \[ x + 3 = 0 \quad \Rightarrow \quad x = -3 \] \[ x - 1 = 0 \quad \Rightarrow \quad x = 1 \]

Final Answer