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

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

Move $12 x$ to the left side of the equation by subtracting it from both sides.

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

Factor using the perfect square rule.

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Rearrange terms.

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

Rewrite $4 x^{2}$ as ${(2 x)}^{2}$ .

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

Rewrite $9$ as $3^{2}$ .

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

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

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

Simplify.

$2 a b = - 12 x$

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

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

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

$2 x - 3 = 0$

Solve for $x$ .

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Add $3$ to both sides of the equation.

$2 x = 3$

Divide each term by $2$ and simplify.

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

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

Cancel the common factor of $2$ .

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Cancel the common factor.

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

Divide $x$ by $1$ .

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

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

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