Quadratic equations by facotring

souls somebody please whow me hot to work out these eqautions by factoring?

8y^2 + 12y - 36 = 0
4b^2 + 2b - 12 = 0
3t^2 - 18t + 15 = 0
2x^2 + 3x - 2 = 0

8y^(2)+12y-36=0

Factor out the GCF of 4 from 8y^(2)+12y-36.
4(2y^(2)+3y-9)=0

Find the factors such that the product of the factors is the trinomial 2y^(2)+3y-9. This can be done by trial and error and checked using the FOIL method of simplifying polynomials.
4(y+3)(2y-3)=0

Divide both sides of the equation by 4. Dividing 0 by any non-zero number is 0.
(y+3)(2y-3)=0

Set each of the factors of the left-hand side of the equation equal to 0.
y+3=0_2y-3=0

Since 3 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 3 from both sides.
y=-3_2y-3=0

Set each of the factors of the left-hand side of the equation equal to 0.
y=-3_2y-3=0

Since -3 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 3 to both sides.
y=-3_2y=3

Divide each term in the equation by 2.
y=-3_y=(3)/(2)

The complete solution is the set of the individual solutions.
y=-3,(3)/(2)
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4b^(2)+2b-12=0

Factor out the GCF of 2 from 4b^(2)+2b-12.
2(2b^(2)+b-6)=0

Find the factors such that the product of the factors is the trinomial 2b^(2)+b-6. This can be done by trial and error and checked using the FOIL method of simplifying polynomials.
2(b+2)(2b-3)=0

Divide both sides of the equation by 2. Dividing 0 by any non-zero number is 0.
(b+2)(2b-3)=0

Set each of the factors of the left-hand side of the equation equal to 0.
b+2=0_2b-3=0

Since 2 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 2 from both sides.
b=-2_2b-3=0

Set each of the factors of the left-hand side of the equation equal to 0.