Solve x (2(x-2))/3=5x/4

Evaluate

x \times \frac{2 ( x - 2 )}{3} = 5 \times \frac{x}{4}

Multiply the terms

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\frac{2 x ( x - 2 )}{3} = 5 \times \frac{x}{4}

Multiply the terms

\frac{2 x ( x - 2 )}{3} = \frac{5 x}{4}

Multiply both sides of the equation by LCD

\frac{2 x ( x - 2 )}{3} \times 12 = \frac{5 x}{4} \times 12

Simplify the equation

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8 x^{2} - 16 x = \frac{5 x}{4} \times 12

Simplify the equation

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8 x^{2} - 16 x = 15 x

Move the expression to the left side

8 x^{2} - 31 x = 0

Factor the expression

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x (8 x - 31) = 0

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

8 x - 31 = 0 x = 0

Solve the equation for x

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x = \frac{31}{8} x = 0

Solution

x_{1} = 0, x_{2} = \frac{31}{8}

Alternative Form

x_{1} = 0, x_{2} = 3.875

Solve the quadratic equation