Solve by Factoring 24x^2+6=24x

$24 x^{2} + 6 = 24 x$

Step 1

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

$24 x^{2} + 6 - 24 x = 0$

Step 2

Factor $6$ out of $24 x^{2} + 6 - 24 x$ .

Factor $6$ out of $24 x^{2}$ .

$6 (4 x^{2}) + 6 - 24 x = 0$

Factor $6$ out of $6$ .

$6 (4 x^{2}) + 6 (1) - 24 x = 0$

Factor $6$ out of $- 24 x$ .

$6 (4 x^{2}) + 6 (1) + 6 (- 4 x) = 0$

Factor $6$ out of $6 (4 x^{2}) + 6 (1)$ .

$6 (4 x^{2} + 1) + 6 (- 4 x) = 0$

Factor $6$ out of $6 (4 x^{2} + 1) + 6 (- 4 x)$ .

$6 (4 x^{2} + 1 - 4 x) = 0$

Step 3

Factor using the perfect square rule.

Rearrange terms.

$6 (4 x^{2} - 4 x + 1) = 0$

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

$6 ({(2 x)}^{2} - 4 x + 1) = 0$

Rewrite $1$ as $1^{2}$ .

$6 ({(2 x)}^{2} - 4 x + 1^{2}) = 0$

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$4 x = 2 \cdot (2 x) \cdot 1$

Rewrite the polynomial.

$6 ({(2 x)}^{2} - 2 \cdot (2 x) \cdot 1 + 1^{2}) = 0$

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = 2 x$ and $b = 1$ .

$6 {(2 x - 1)}^{2} = 0$

Step 4

Divide each term in $6 {(2 x - 1)}^{2} = 0$ by $6$ and simplify.

Divide each term in $6 {(2 x - 1)}^{2} = 0$ by $6$ .

$\frac{6 {(2 x - 1)}^{2}}{6} = \frac{0}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 {(2 x - 1)}^{2}}{6} = \frac{0}{6}$

Divide ${(2 x - 1)}^{2}$ by $1$ .

${(2 x - 1)}^{2} = \frac{0}{6}$

Simplify the right side.

Divide $0$ by $6$ .

${(2 x - 1)}^{2} = 0$

Step 5

Set the $2 x - 1$ equal to $0$ .

$2 x - 1 = 0$

Step 6

Solve for $x$ .

Add $1$ to both sides of the equation.

$2 x = 1$

Divide each term in $2 x = 1$ by $2$ and simplify.

Divide each term in $2 x = 1$ by $2$ .

$\frac{2 x}{2} = \frac{1}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{1}{2}$

Divide $x$ by $1$ .

$x = \frac{1}{2}$

Solve by Factoring 24x^2+6=24x

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