Solve Using the Quadratic Formula (7y+26)(4y+7)=0

$(7 y + 26) (4 y + 7) = 0$

Step 1

Simplify the left side.

Simplify $(7 y + 26) (4 y + 7)$ .

Expand $(7 y + 26) (4 y + 7)$ using the FOIL Method.

Apply the distributive property.

$7 y (4 y + 7) + 26 (4 y + 7) = 0$

Apply the distributive property.

$7 y (4 y) + 7 y \cdot 7 + 26 (4 y + 7) = 0$

Apply the distributive property.

$7 y (4 y) + 7 y \cdot 7 + 26 (4 y) + 26 \cdot 7 = 0$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$7 \cdot 4 y \cdot y + 7 y \cdot 7 + 26 (4 y) + 26 \cdot 7 = 0$

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$7 \cdot 4 (y \cdot y) + 7 y \cdot 7 + 26 (4 y) + 26 \cdot 7 = 0$

Multiply $y$ by $y$ .

$7 \cdot 4 y^{2} + 7 y \cdot 7 + 26 (4 y) + 26 \cdot 7 = 0$

Multiply $7$ by $4$ .

$28 y^{2} + 7 y \cdot 7 + 26 (4 y) + 26 \cdot 7 = 0$

Multiply $7$ by $7$ .

$28 y^{2} + 49 y + 26 (4 y) + 26 \cdot 7 = 0$

Multiply $4$ by $26$ .

$28 y^{2} + 49 y + 104 y + 26 \cdot 7 = 0$

Multiply $26$ by $7$ .

$28 y^{2} + 49 y + 104 y + 182 = 0$

Add $49 y$ and $104 y$ .

$28 y^{2} + 153 y + 182 = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = 28$ , $b = 153$ , and $c = 182$ into the quadratic formula and solve for $y$ .

$\frac{- 153 \pm \sqrt{153^{2} - 4 \cdot (28 \cdot 182)}}{2 \cdot 28}$

Step 4

Simplify.

Simplify the numerator.

Raise $153$ to the power of $2$ .

$y = \frac{- 153 \pm \sqrt{23409 - 4 \cdot 28 \cdot 182}}{2 \cdot 28}$

Multiply $- 4 \cdot 28 \cdot 182$ .

Multiply $- 4$ by $28$ .

$y = \frac{- 153 \pm \sqrt{23409 - 112 \cdot 182}}{2 \cdot 28}$

Multiply $- 112$ by $182$ .

$y = \frac{- 153 \pm \sqrt{23409 - 20384}}{2 \cdot 28}$

Subtract $20384$ from $23409$ .

$y = \frac{- 153 \pm \sqrt{3025}}{2 \cdot 28}$

Rewrite $3025$ as $55^{2}$ .

$y = \frac{- 153 \pm \sqrt{55^{2}}}{2 \cdot 28}$

Pull terms out from under the radical, assuming positive real numbers.

$y = \frac{- 153 \pm 55}{2 \cdot 28}$

Multiply $2$ by $28$ .

$y = \frac{- 153 \pm 55}{56}$

Step 5

The final answer is the combination of both solutions.

$y = - \frac{7}{4}, - \frac{26}{7}$

Solve Using the Quadratic Formula (7y+26)(4y+7)=0

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