Solve for x 10x=4x^2-6

$10 x = 4 x^{2} - 6$

Subtract $4 x^{2}$ from both sides of the equation.

$10 x - 4 x^{2} = - 6$

Add $6$ to both sides of the equation.

$10 x - 4 x^{2} + 6 = 0$

Factor the left side of the equation.

Factor $- 2$ out of $10 x - 4 x^{2} + 6$ .

Reorder $10 x$ and $- 4 x^{2}$ .

$- 4 x^{2} + 10 x + 6 = 0$

Factor $- 2$ out of $- 4 x^{2}$ .

$- 2 (2 x^{2}) + 10 x + 6 = 0$

Factor $- 2$ out of $10 x$ .

$- 2 (2 x^{2}) - 2 (- 5 x) + 6 = 0$

Factor $- 2$ out of $6$ .

$- 2 (2 x^{2}) - 2 (- 5 x) - 2 \cdot - 3 = 0$

Factor $- 2$ out of $- 2 (2 x^{2}) - 2 (- 5 x)$ .

$- 2 (2 x^{2} - 5 x) - 2 \cdot - 3 = 0$

Factor $- 2$ out of $- 2 (2 x^{2} - 5 x) - 2 (- 3)$ .

$- 2 (2 x^{2} - 5 x - 3) = 0$

Factor.

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 2 \cdot - 3 = - 6$ and whose sum is $b = - 5$ .

Factor $- 5$ out of $- 5 x$ .

$- 2 (2 x^{2} - 5 x - 3) = 0$

Rewrite $- 5$ as $1$ plus $- 6$

$- 2 (2 x^{2} + (1 - 6) x - 3) = 0$

Apply the distributive property.

$- 2 (2 x^{2} + 1 x - 6 x - 3) = 0$

Multiply $x$ by $1$ .

$- 2 (2 x^{2} + x - 6 x - 3) = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$- 2 ((2 x^{2} + x) - 6 x - 3) = 0$

Factor out the greatest common factor (GCF) from each group.

$- 2 (x (2 x + 1) - 3 (2 x + 1)) = 0$

Factor the polynomial by factoring out the greatest common factor, $2 x + 1$ .

$- 2 ((2 x + 1) (x - 3)) = 0$

Remove unnecessary parentheses.

$- 2 (2 x + 1) (x - 3) = 0$

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

$2 x + 1 = 0$

$x - 3 = 0$

Set $2 x + 1$ equal to $0$ and solve for $x$ .

Set $2 x + 1$ equal to $0$ .

$2 x + 1 = 0$

Solve $2 x + 1 = 0$ for $x$ .

Subtract $1$ from 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 $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

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 $- 2 (2 x + 1) (x - 3) = 0$ true.

$x = - \frac{1}{2}, 3$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{1}{2}, 3$

Decimal Form:

$x = - 0.5, 3$

Solve for x 10x=4x^2-6

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