Solve for x

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x\left(3x-24\right)=0
Factor out x.
x=0 x=8
To find equation solutions, solve x=0 and 3x-24=0.
3x^{2}-24x=0
All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.
x=\frac{-\left(-24\right)±\sqrt{\left(-24\right)^{2}}}{2\times 3}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, -24 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-\left(-24\right)±24}{2\times 3}
Take the square root of \left(-24\right)^{2}\approx 576.
x=\frac{24±24}{2\times 3}
The opposite of -24 is 24.
x=\frac{24±24}{6}
Multiply 2 times 3.
x=\frac{48}{6}
Now solve the equation x=\frac{24±24}{6} when ± is plus. Add 24 to 24.
x=8
Divide 48 by 6.
x=\frac{0}{6}
Now solve the equation x=\frac{24±24}{6} when ± is minus. Subtract 24 from 24.
x=0
Divide 0 by 6.
x=8 x=0
The equation is now solved.
3x^{2}-24x=0
Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.
\frac{3x^{2}-24x}{3}=\frac{0}{3}
Divide both sides by 3.
x^{2}+\frac{-24}{3}x=\frac{0}{3}
Dividing by 3 undoes the multiplication by 3.
x^{2}-8x=\frac{0}{3}
Divide -24 by 3.
x^{2}-8x=0
Divide 0 by 3.
x^{2}-8x+\left(-4\right)^{2}=\left(-4\right)^{2}
Divide -8, the coefficient of the x term, by 2 to get -4. Then add the square of -4 to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x^{2}-8x+16=16
Square -4.
\left(x-4\right)^{2}=16
Factor x^{2}-8x+16. 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-4\right)^{2}}=\sqrt{16}
Take the square root of both sides of the equation.
x-4=4 x-4=-4
Simplify.
x=8 x=0
Add 4 to both sides of the equation.