1Cademy - Solving $$(3x - 8)(x

Example

Solving $(3x - 8)(x - 1) = 3x$

Solve $(3x - 8)(x - 1) = 3x$ by first multiplying the binomials and then writing the quadratic equation in standard form.

Step 1 — Multiply the binomials: Expand the left side using FOIL: $3x^2 - 11x + 8 = 3x$

Step 2 — Write in standard form: Subtract $3x$ from both sides to set the equation to zero: $3x^2 - 14x + 8 = 0$

Step 3 — Factor the trinomial: $(3x - 2)(x - 4) = 0$

Step 4 — Apply the Zero Product Property: Set each factor to zero: $3x - 2 = 0 \quad \text{or} \quad x - 4 = 0$

Step 5 — Solve each equation: $3x = 2 \implies x = \frac{2}{3} \quad \text{or} \quad x = 4$

Step 6 — Check: The check is left as an exercise. The solutions are $x = \frac{2}{3}$ and $x = 4$ .

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Updated 2026-04-30

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