Solve (5x)/2=2x (x-2)/3

Evaluate

\frac{5 x}{2} = 2 x \times \frac{x - 2}{3}

Multiply the terms

\frac{5 x}{2} = \frac{2 x ( x - 2 )}{3}

Swap the sides

\frac{2 x ( x - 2 )}{3} = \frac{5 x}{2}

Multiply both sides of the equation by LCD

\frac{2 x ( x - 2 )}{3} \times 6 = \frac{5 x}{2} \times 6

Simplify the equation

More Steps

4 x^{2} - 8 x = \frac{5 x}{2} \times 6

Simplify the equation

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4 x^{2} - 8 x = 15 x

Move the expression to the left side

4 x^{2} - 23 x = 0

Factor the expression

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x (4 x - 23) = 0

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

4 x - 23 = 0 x = 0

Solve the equation for x

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x = \frac{23}{4} x = 0

Solution

x_{1} = 0, x_{2} = \frac{23}{4}

Alternative Form

x_{1} = 0, x_{2} = 5.75

Solve the quadratic equation