Solve by Factoring 5x^2+19x-4=(5x-1)

$5 x^{2} + 19 x - 4 = (5 x - 1)$

Step 1

Subtract $(5 x - 1)$ from both sides of the equation.

$5 x^{2} + 19 x - 4 - (5 x - 1) = 0$

Step 2

Simplify $5 x^{2} + 19 x - 4 - (5 x - 1)$ .

Simplify each term.

Apply the distributive property.

$5 x^{2} + 19 x - 4 - (5 x) - - 1 = 0$

Multiply $5$ by $- 1$ .

$5 x^{2} + 19 x - 4 - 5 x - - 1 = 0$

Multiply $- 1$ by $- 1$ .

$5 x^{2} + 19 x - 4 - 5 x + 1 = 0$

Subtract $5 x$ from $19 x$ .

$5 x^{2} + 14 x - 4 + 1 = 0$

Add $- 4$ and $1$ .

$5 x^{2} + 14 x - 3 = 0$

Step 3

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 $b = 14$ .

Factor $14$ out of $14 x$ .

$5 x^{2} + 14 (x) - 3 = 0$

Rewrite $14$ 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, $5 x - 1$ .

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

Step 4

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

$5 x - 1 = 0$

$x + 3 = 0$

Step 5

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 $1$ .

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

Step 6

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

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

$x + 3 = 0$

Subtract $3$ from both sides of the equation.

$x = - 3$

Step 7

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+19x-4=(5x-1)

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