Questions: Equations and Inequalities Finding the roots of a quadratic equation of the form ax^2+bx=0 Solve for x. 6 x^2=12 x If there is more than one solution, separate them with commas. If there is no solution, click on "No solution". x=

Equations and Inequalities
Finding the roots of a quadratic equation of the form ax^2+bx=0

Solve for x.

6 x^2=12 x

If there is more than one solution, separate them with commas. If there is no solution, click on "No solution".

x=
Transcript text: Equations and Inequalities Finding the roots of a quadratic equation of the form $a x^{2}+b x=0$ Solve for $x$. \[ 6 x^{2}=12 x \] If there is more than one solution, separate them with commas. If there is no solution, click on "No solution". $\square$ \[ x= \]
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Solution

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Solve for \(x\). \(6x^2 = 12x\)

Rewrite the equation

We are given the equation \(6x^2 = 12x\). We rewrite this as: \(6x^2 - 12x = 0\)

Factor the equation

We factor out \(6x\) from both terms on the left side of the equation: \(6x(x-2) = 0\)

Solve for x

Set each factor equal to zero and solve for \(x\). \(6x = 0 \implies x = 0\) \(x-2 = 0 \implies x = 2\)

\(\boxed{x = 0, 2}\)

\(\boxed{x = 0, 2}\)

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