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Question 325859: Solve by factoring and using the principle of zero products. Show all work necessary.
4x^2 - 12x = 16
Answer by Apathious(24)   (Show Source):
You can put this solution on YOUR website! 4x^(2)-12x=16
To set the left-hand side of the equation equal to 0, move all the expressions to the left-hand side.
4x^(2)-12x-16=0
Factor out the GCF of 4 from each term in the polynomial.
4(x^(2))+4(-3x)+4(-4)=0
Factor out the GCF of 4 from 4x^(2)-12x-16.
4(x^(2)-3x-4)=0
For a polynomial of the form x^(2)+bx+c, find two factors of c (-4) that add up to b (-3). In this problem 1*-4=-4 and 1-4=-3, so insert 1 as the right hand term of one factor and -4 as the right-hand term of the other factor.
4(x+1)(x-4)=0
Divide both sides of the equation by 4. Dividing 0 by any non-zero number is 0.
(x+1)(x-4)=0
Set each of the factors of the left-hand side of the equation equal to 0.
x+1=0_x-4=0
Since 1 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 1 from both sides.
x=-1_x-4=0
Set each of the factors of the left-hand side of the equation equal to 0.
x=-1_x-4=0
Since -4 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 4 to both sides.
x=-1_x=4
The complete solution is the set of the individual solutions.
x=-1,4
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