Solve for w 64w^2+96w+36=0

$64 w^{2} + 96 w + 36 = 0$

Factor the left side of the equation.

Factor $4$ out of $64 w^{2} + 96 w + 36$ .

Factor $4$ out of $64 w^{2}$ .

$4 (16 w^{2}) + 96 w + 36 = 0$

Factor $4$ out of $96 w$ .

$4 (16 w^{2}) + 4 (24 w) + 36 = 0$

Factor $4$ out of $36$ .

$4 (16 w^{2}) + 4 (24 w) + 4 (9) = 0$

Factor $4$ out of $4 (16 w^{2}) + 4 (24 w)$ .

$4 (16 w^{2} + 24 w) + 4 (9) = 0$

Factor $4$ out of $4 (16 w^{2} + 24 w) + 4 (9)$ .

$4 (16 w^{2} + 24 w + 9) = 0$

Factor using the perfect square rule.

Rewrite $16 w^{2}$ as ${(4 w)}^{2}$ .

$4 ({(4 w)}^{2} + 24 w + 9) = 0$

Rewrite $9$ as $3^{2}$ .

$4 ({(4 w)}^{2} + 24 w + 3^{2}) = 0$

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$24 w = 2 \cdot (4 w) \cdot 3$

Rewrite the polynomial.

$4 ({(4 w)}^{2} + 2 \cdot (4 w) \cdot 3 + 3^{2}) = 0$

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = 4 w$ and $b = 3$ .

$4 {(4 w + 3)}^{2} = 0$

Divide each term in $4 {(4 w + 3)}^{2} = 0$ by $4$ and simplify.

Divide each term in $4 {(4 w + 3)}^{2} = 0$ by $4$ .

$\frac{4 {(4 w + 3)}^{2}}{4} = \frac{0}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 {(4 w + 3)}^{2}}{4} = \frac{0}{4}$

Divide ${(4 w + 3)}^{2}$ by $1$ .

${(4 w + 3)}^{2} = \frac{0}{4}$

Simplify the right side.

Divide $0$ by $4$ .

${(4 w + 3)}^{2} = 0$

Set the $4 w + 3$ equal to $0$ .

$4 w + 3 = 0$

Solve for $w$ .

Subtract $3$ from both sides of the equation.

$4 w = - 3$

Divide each term in $4 w = - 3$ by $4$ and simplify.

Divide each term in $4 w = - 3$ by $4$ .

$\frac{4 w}{4} = \frac{- 3}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 w}{4} = \frac{- 3}{4}$

Divide $w$ by $1$ .

$w = \frac{- 3}{4}$

Simplify the right side.

Move the negative in front of the fraction.

$w = - \frac{3}{4}$

The result can be shown in multiple forms.

Exact Form:

$w = - \frac{3}{4}$

Decimal Form:

$w = - 0.75$

Solve for w 64w^2+96w+36=0

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