Solve for c 25c^2-5c-16=-4

$25 c^{2} - 5 c - 16 = - 4$

Step 1

Add $4$ to both sides of the equation.

$25 c^{2} - 5 c - 16 + 4 = 0$

Step 2

Add $- 16$ and $4$ .

$25 c^{2} - 5 c - 12 = 0$

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 $a \cdot c = 25 \cdot - 12 = - 300$ and whose sum is $b = - 5$ .

Factor $- 5$ out of $- 5 c$ .

$25 c^{2} - 5 c - 12 = 0$

Rewrite $- 5$ as $15$ plus $- 20$

$25 c^{2} + (15 - 20) c - 12 = 0$

Apply the distributive property.

$25 c^{2} + 15 c - 20 c - 12 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(25 c^{2} + 15 c) - 20 c - 12 = 0$

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

$5 c (5 c + 3) - 4 (5 c + 3) = 0$

Factor the polynomial by factoring out the greatest common factor, $5 c + 3$ .

$(5 c + 3) (5 c - 4) = 0$

Step 4

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

$5 c + 3 = 0$

$5 c - 4 = 0$

Step 5

Set $5 c + 3$ equal to $0$ and solve for $c$ .

Set $5 c + 3$ equal to $0$ .

$5 c + 3 = 0$

Solve $5 c + 3 = 0$ for $c$ .

Subtract $3$ from both sides of the equation.

$5 c = - 3$

Divide each term in $5 c = - 3$ by $5$ and simplify.

Divide each term in $5 c = - 3$ by $5$ .

$\frac{5 c}{5} = \frac{- 3}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 c}{5} = \frac{- 3}{5}$

Divide $c$ by $1$ .

$c = \frac{- 3}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$c = - \frac{3}{5}$

Step 6

Set $5 c - 4$ equal to $0$ and solve for $c$ .

Set $5 c - 4$ equal to $0$ .

$5 c - 4 = 0$

Solve $5 c - 4 = 0$ for $c$ .

Add $4$ to both sides of the equation.

$5 c = 4$

Divide each term in $5 c = 4$ by $5$ and simplify.

Divide each term in $5 c = 4$ by $5$ .

$\frac{5 c}{5} = \frac{4}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 c}{5} = \frac{4}{5}$

Divide $c$ by $1$ .

$c = \frac{4}{5}$

Step 7

The final solution is all the values that make $(5 c + 3) (5 c - 4) = 0$ true.

$c = - \frac{3}{5}, \frac{4}{5}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$c = - \frac{3}{5}, \frac{4}{5}$

Decimal Form:

$c = - 0.6, 0.8$

Solve for c 25c^2-5c-16=-4

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