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3x^{2}-4x-4=\left(x-4\right)\left(2x+1\right)
Use the distributive property to multiply x-2 by 3x+2 and combine like terms.
3x^{2}-4x-4=2x^{2}-7x-4
Use the distributive property to multiply x-4 by 2x+1 and combine like terms.
3x^{2}-4x-4-2x^{2}=-7x-4
Subtract 2x^{2} from both sides.
x^{2}-4x-4=-7x-4
Combine 3x^{2} and -2x^{2} to get x^{2}.
x^{2}-4x-4+7x=-4
Add 7x to both sides.
x^{2}+3x-4=-4
Combine -4x and 7x to get 3x.
x^{2}+3x-4+4=0
Add 4 to both sides.
x^{2}+3x=0
Add -4 and 4 to get 0.
x=\frac{-3±\sqrt{3^{2}}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 3 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-3±3}{2}
Take the square root of 3^{2}.
x=\frac{0}{2}
Now solve the equation x=\frac{-3±3}{2} when ± is plus. Add -3 to 3.
x=0
Divide 0 by 2.
x=-\frac{6}{2}
Now solve the equation x=\frac{-3±3}{2} when ± is minus. Subtract 3 from -3.
x=-3
Divide -6 by 2.
x=0 x=-3
The equation is now solved.
3x^{2}-4x-4=\left(x-4\right)\left(2x+1\right)
Use the distributive property to multiply x-2 by 3x+2 and combine like terms.
3x^{2}-4x-4=2x^{2}-7x-4
Use the distributive property to multiply x-4 by 2x+1 and combine like terms.
3x^{2}-4x-4-2x^{2}=-7x-4
Subtract 2x^{2} from both sides.
x^{2}-4x-4=-7x-4
Combine 3x^{2} and -2x^{2} to get x^{2}.
x^{2}-4x-4+7x=-4
Add 7x to both sides.
x^{2}+3x-4=-4
Combine -4x and 7x to get 3x.
x^{2}+3x=-4+4
Add 4 to both sides.
x^{2}+3x=0
Add -4 and 4 to get 0.
x^{2}+3x+\left(\frac{3}{2}\right)^{2}=\left(\frac{3}{2}\right)^{2}
Divide 3, the coefficient of the x term, by 2 to get \frac{3}{2}. Then add the square of \frac{3}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x^{2}+3x+\frac{9}{4}=\frac{9}{4}
Square \frac{3}{2} by squaring both the numerator and the denominator of the fraction.
\left(x+\frac{3}{2}\right)^{2}=\frac{9}{4}
Factor x^{2}+3x+\frac{9}{4}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.
\sqrt{\left(x+\frac{3}{2}\right)^{2}}=\sqrt{\frac{9}{4}}
Take the square root of both sides of the equation.
x+\frac{3}{2}=\frac{3}{2} x+\frac{3}{2}=-\frac{3}{2}
Simplify.
x=0 x=-3
Subtract \frac{3}{2} from both sides of the equation.