Solve by Factoring 9x^2-12x+4=0

$9 x^{2} - 12 x + 4 = 0$

Factor using the perfect square rule.

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Rewrite $9 x^{2}$ as ${(3 x)}^{2}$ .

${(3 x)}^{2} - 12 x + 4 = 0$

Rewrite $4$ as $2^{2}$ .

${(3 x)}^{2} - 12 x + 2^{2} = 0$

Check the middle term by multiplying $2 a b$ and compare this result with the middle term in the original expression.

$2 a b = 2 \cdot (3 x) \cdot - 2$

Simplify.

$2 a b = - 12 x$

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = 3 x$ and $b = - 2$ .

${(3 x - 2)}^{2} = 0$

Set the $3 x - 2$ equal to $0$ .

$3 x - 2 = 0$

Solve for $x$ .

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Add $2$ to both sides of the equation.

$3 x = 2$

Divide each term by $3$ and simplify.

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Divide each term in $3 x = 2$ by $3$ .

$\frac{3 x}{3} = \frac{2}{3}$

Cancel the common factor of $3$ .

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Cancel the common factor.

$\frac{3 x}{3} = \frac{2}{3}$

Divide $x$ by $1$ .

$x = \frac{2}{3}$

Solve by Factoring 9x^2-12x+4=0

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