Find the Roots (Zeros) (5b-4)(b+3)=0

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

Step 1

Simplify $(5 b - 4) (b + 3)$ .

Expand $(5 b - 4) (b + 3)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

$5 b \cdot b + 5 b \cdot 3 - 4 (b + 3) = 0$

Apply the distributive property.

$5 b \cdot b + 5 b \cdot 3 - 4 b - 4 \cdot 3 = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $b$ by $b$ by adding the exponents.

Move $b$ .

$5 (b \cdot b) + 5 b \cdot 3 - 4 b - 4 \cdot 3 = 0$

Multiply $b$ by $b$ .

$5 b^{2} + 5 b \cdot 3 - 4 b - 4 \cdot 3 = 0$

Multiply $3$ by $5$ .

$5 b^{2} + 15 b - 4 b - 4 \cdot 3 = 0$

Multiply $- 4$ by $3$ .

$5 b^{2} + 15 b - 4 b - 12 = 0$

Subtract $4 b$ from $15 b$ .

$5 b^{2} + 11 b - 12 = 0$

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 $a \cdot c = 5 \cdot - 12 = - 60$ and whose sum is $b = 11$ .

Factor $11$ out of $11 b$ .

$5 b^{2} + 11 (b) - 12 = 0$

Rewrite $11$ as $- 4$ plus $15$

$5 b^{2} + (- 4 + 15) b - 12 = 0$

Apply the distributive property.

$5 b^{2} - 4 b + 15 b - 12 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(5 b^{2} - 4 b) + 15 b - 12 = 0$

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

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

Factor the polynomial by factoring out the greatest common factor, $5 b - 4$ .

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

Step 3

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

$5 b - 4 = 0$

$b + 3 = 0$

Step 4

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

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

$5 b - 4 = 0$

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

Add $4$ to both sides of the equation.

$5 b = 4$

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

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

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

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

Divide $b$ by $1$ .

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

Step 5

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

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

$b + 3 = 0$

Subtract $3$ from both sides of the equation.

$b = - 3$

Step 6

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

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

Step 7

Find the Roots (Zeros) (5b-4)(b+3)=0

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