Solve x/2 x/3=(x 7)/3

Evaluate

\frac{x}{2} \times \frac{x}{3} = \frac{x \times 7}{3}

Multiply the terms

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\frac{x ^{2}}{6} = \frac{x \times 7}{3}

Use the commutative property to reorder the terms

\frac{x ^{2}}{6} = \frac{7 x}{3}

Multiply both sides of the equation by LCD

\frac{x ^{2}}{6} \times 6 = \frac{7 x}{3} \times 6

Simplify the equation

x^{2} = \frac{7 x}{3} \times 6

Simplify the equation

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x^{2} = 14 x

Move the expression to the left side

x^{2} - 14 x = 0

Factor the expression

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x (x - 14) = 0

When the product of factors equals 0,at least one factor is 0

x - 14 = 0 x = 0

Solve the equation for x

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x = 14 x = 0

Solution

x_{1} = 0, x_{2} = 14

Solve the quadratic equation