# Solve by factorization 6x^{2}+x-2=0

Solve by factorization
$6{x}^{2}+x-2=0$
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John Koga
Step 1
factor the following $6{x}^{2}+x-2=0$
Step 2
Factor the quadratic $6{x}^{2}+x-2$
The coefficient of ${x}^{2}$ is 6 and the constant term is -2.
The product of 6 and -2 is -12. The factors of -12 which sum to 1 are -3 and 4.
So $6{x}^{2}+x-2=6{x}^{2}+4x-3x-2=2\left(2x-1\right)+3x\left(2x-1\right):$
2(2x-1)+3x(2x-1):
Factor 2x-1 from 2(2x-1)+3x(2x-1)=(2x-1)(3x+2);
=(2x-1)(3x+2)
Now set (2x-1)(3x+2)=0
(2x-1)=0 and (3x+2)=0

Samantha Brown
Step 1
The given equation is
$6{x}^{2}+x-2=0$
Step 2
$6{x}^{2}+\left(4-3\right)x-2=0$
$6{x}^{2}+4x-3x-2=0$
$2{x}^{\cdot }\left(3x+2\right)-{1}^{\cdot }\left(3x+2\right)=0$
${\left(3x+2\right)}^{\cdot }\left(2x-1\right)=0$
So
(3x+2)=0. Or (2x-1)=0
x=-2/3, 1/2