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GMAT - Problem Solving - Algebra

If x(2x+1)=0 and (x+1/2)(2x-3)=0, then x=

If x(2x 1)=0 and (x 1/2)(2x-3)=0, then x=?

Equation 1

x(2x+1)=0

2x2 + x = 0

x (2x + 1) = 0

x = 0 or x = -1/2

Equation 2

(x+1/2)(2x-3) = 0

2x2 - 3x + x - 3/2 = 0

2x2 - 2x - 3/2 = 0

4x2 - 4x - 3 = 0

4x2 - 6x + 2x - 3 = 0

2x (2x - 3) + (2x - 3) = 0

(2x - 3) (2x + 1) = 0

x = 3/2 or x = -1/2

x = -1/2 satisfies both the equation

hence answer is x = -1/2

Equation 1

x(2x+1)=0

2x2 + x = 0

x (2x + 1) = 0

x = 0 or x = -1/2

Equation 2

(x+1/2)(2x-3) = 0

2x2 - 3x + x - 3/2 = 0

2x2 - 2x - 3/2 = 0

4x2 - 4x - 3 = 0

4x2 - 6x + 2x - 3 = 0

2x (2x - 3) + (2x - 3) = 0

(2x - 3) (2x + 1) = 0

x = 3/2 or x = -1/2

x = -1/2 satisfies both the equation

hence answer is x = -1/2