Product of 2 binomials is 0

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The only way a product can equal zero is if one of the factors is zero.
Two nonzero numbers always multiply to something nonzero.
So (A)(B)=0(A)(B) = 0 forces A=0A = 0 or B=0B = 0.
This is why a factored equation is easy to solve.
Set each factor equal to zero on its own.
Each little equation you solve gives one possible value of the variable.
Take x(3x−2)=0x(3x - 2) = 0.
One factor is xx and the other is 3x−23x - 2.
Setting each to zero gives x=0x = 0, or 3x−2=03x - 2 = 0 which gives x=23x = \frac{2}{3}.
A product of two binomials set to zero usually gives two solutions, one from each factor.
For (2x+1)(x+2)=0(2x + 1)(x + 2) = 0, solve them separately.
2x+1=02x + 1 = 0 gives x=−12x = -\frac{1}{2}, and x+2=0x + 2 = 0 gives x=−2x = -2.

Worked examples

Solve (x−5)(x+4)=0(x - 5)(x + 4) = 0.
Set each factor to zero: x−5=0x - 5 = 0 or x+4=0x + 4 = 0.
So x=5x = 5 or x=−4x = -4.
Solve x(2x−6)=0x(2x - 6) = 0.
Set each factor to zero: x=0x = 0 or 2x−6=02x - 6 = 0.
So x=0x = 0 or x=3x = 3.
Solve (3x+2)(x−1)=0(3x + 2)(x - 1) = 0.
Set each factor to zero: 3x+2=03x + 2 = 0 or x−1=0x - 1 = 0.
So x=−23x = -\frac{2}{3} or x=1x = 1.

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