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In this lesson we solve x squared minus five x plus six equals zero by factoring.

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Factoring turns one quadratic equation into two simple linear ones.

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The equation is already in standard form, with zero on the right.

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We need two numbers that multiply to positive six and add to negative five.

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Negative two and negative three work: their product is six and their sum is negative five.

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So the left side factors as x minus two, times x minus three.

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If a product is zero, at least one of the factors must be zero.

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That gives x equals two, or x equals three.

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The graph of y equals x squared minus five x plus six crosses the x axis at exactly two places.

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Those crossings, at two and at three, are the solutions we found.

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Check x equals two: four minus ten plus six is zero.

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Check x equals three: nine minus fifteen plus six is also zero, so both answers work.

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To recap: get zero on one side, factor, and set each factor equal to zero.

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Then check every answer in the original equation.