Solve by Factoring 14x^2=25x+25

$14 x^{2} = 25 x + 25$

Step 1

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

Subtract $25 x$ from both sides of the equation.

$14 x^{2} - 25 x = 25$

Subtract $25$ from both sides of the equation.

$14 x^{2} - 25 x - 25 = 0$

Step 2

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 $a \cdot c = 14 \cdot - 25 = - 350$ and whose sum is $b = - 25$ .

Factor $- 25$ out of $- 25 x$ .

$14 x^{2} - 25 x - 25 = 0$

Rewrite $- 25$ as $10$ plus $- 35$

$14 x^{2} + (10 - 35) x - 25 = 0$

Apply the distributive property.

$14 x^{2} + 10 x - 35 x - 25 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(14 x^{2} + 10 x) - 35 x - 25 = 0$

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

$2 x (7 x + 5) - 5 (7 x + 5) = 0$

Factor the polynomial by factoring out the greatest common factor, $7 x + 5$ .

$(7 x + 5) (2 x - 5) = 0$

Step 3

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

$7 x + 5 = 0$

$2 x - 5 = 0$

Step 4

Set $7 x + 5$ equal to $0$ and solve for $x$ .

Set $7 x + 5$ equal to $0$ .

$7 x + 5 = 0$

Solve $7 x + 5 = 0$ for $x$ .

Subtract $5$ from both sides of the equation.

$7 x = - 5$

Divide each term in $7 x = - 5$ by $7$ and simplify.

Divide each term in $7 x = - 5$ by $7$ .

$\frac{7 x}{7} = \frac{- 5}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{- 5}{7}$

Divide $x$ by $1$ .

$x = \frac{- 5}{7}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{5}{7}$

Step 5

Set $2 x - 5$ equal to $0$ and solve for $x$ .

Set $2 x - 5$ equal to $0$ .

$2 x - 5 = 0$

Solve $2 x - 5 = 0$ for $x$ .

Add $5$ to both sides of the equation.

$2 x = 5$

Divide each term in $2 x = 5$ by $2$ and simplify.

Divide each term in $2 x = 5$ by $2$ .

$\frac{2 x}{2} = \frac{5}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{5}{2}$

Divide $x$ by $1$ .

$x = \frac{5}{2}$

Step 6

The final solution is all the values that make $(7 x + 5) (2 x - 5) = 0$ true.

$x = - \frac{5}{7}, \frac{5}{2}$

Solve by Factoring 14x^2=25x+25

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