Solve by Factoring 5x^2+7=16x+4

$5 x^{2} + 7 = 16 x + 4$

Move all the expressions to the left side of the equation.

Subtract $16 x$ from both sides of the equation.

$5 x^{2} + 7 - 16 x = 4$

Subtract $4$ from both sides of the equation.

$5 x^{2} + 7 - 16 x - 4 = 0$

Subtract $4$ from $7$ .

$5 x^{2} - 16 x + 3 = 0$

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 $a \cdot c = 5 \cdot 3 = 15$ and whose sum is $b = - 16$ .

Factor $- 16$ out of $- 16 x$ .

$5 x^{2} - 16 x + 3 = 0$

Rewrite $- 16$ as $- 1$ plus $- 15$

$5 x^{2} + (- 1 - 15) x + 3 = 0$

Apply the distributive property.

$5 x^{2} - 1 x - 15 x + 3 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(5 x^{2} - 1 x) - 15 x + 3 = 0$

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

$x (5 x - 1) - 3 (5 x - 1) = 0$

Factor the polynomial by factoring out the greatest common factor, $5 x - 1$ .

$(5 x - 1) (x - 3) = 0$

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

$5 x - 1 = 0$

$x - 3 = 0$

Set $5 x - 1$ equal to $0$ and solve for $x$ .

Set $5 x - 1$ equal to $0$ .

$5 x - 1 = 0$

Solve $5 x - 1 = 0$ for $x$ .

Add $1$ to both sides of the equation.

$5 x = 1$

Divide each term in $5 x = 1$ by $5$ and simplify.

Divide each term in $5 x = 1$ by $5$ .

$\frac{5 x}{5} = \frac{1}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{1}{5}$

Divide $x$ by $1$ .

$x = \frac{1}{5}$

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 $(5 x - 1) (x - 3) = 0$ true.

$x = \frac{1}{5}, 3$

Solve by Factoring 5x^2+7=16x+4

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