Find the Roots (Zeros) 3x^2+45=24x

$3 x^{2} + 45 = 24 x$

Subtract $24 x$ from both sides of the equation.

$3 x^{2} + 45 - 24 x = 0$

Factor the left side of the equation.

Factor $3$ out of $3 x^{2} + 45 - 24 x$ .

Factor $3$ out of $3 x^{2}$ .

$3 (x^{2}) + 45 - 24 x = 0$

Factor $3$ out of $45$ .

$3 x^{2} + 3 \cdot 15 - 24 x = 0$

Factor $3$ out of $- 24 x$ .

$3 x^{2} + 3 \cdot 15 + 3 (- 8 x) = 0$

Factor $3$ out of $3 x^{2} + 3 \cdot 15$ .

$3 (x^{2} + 15) + 3 (- 8 x) = 0$

Factor $3$ out of $3 (x^{2} + 15) + 3 (- 8 x)$ .

$3 (x^{2} + 15 - 8 x) = 0$

Factor.

Factor $x^{2} + 15 - 8 x$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $15$ and whose sum is $- 8$ .

$- 5, - 3$

Write the factored form using these integers.

$3 ((x - 5) (x - 3)) = 0$

Remove unnecessary parentheses.

$3 (x - 5) (x - 3) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x - 5 = 0$

$x - 3 = 0$

Set $x - 5$ equal to $0$ and solve for $x$ .

Set $x - 5$ equal to $0$ .

$x - 5 = 0$

Add $5$ to both sides of the equation.

$x = 5$

Set $x - 3$ equal to $0$ and solve for $x$ .

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

$x - 3 = 0$

Add $3$ to both sides of the equation.

$x = 3$

The final solution is all the values that make $3 (x - 5) (x - 3) = 0$ true.

$x = 5, 3$

Find the Roots (Zeros) 3x^2+45=24x

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