Solve for x (3x+4)^2-36=15x+20

${(3 x + 4)}^{2} - 36 = 15 x + 20$

Move all terms containing $x$ to the left side of the equation.

Subtract $15 x$ from both sides of the equation.

${(3 x + 4)}^{2} - 36 - 15 x = 20$

Simplify each term.

Rewrite ${(3 x + 4)}^{2}$ as $(3 x + 4) (3 x + 4)$ .

$(3 x + 4) (3 x + 4) - 36 - 15 x = 20$

Expand $(3 x + 4) (3 x + 4)$ using the FOIL Method.

Apply the distributive property.

$3 x (3 x + 4) + 4 (3 x + 4) - 36 - 15 x = 20$

Apply the distributive property.

$3 x (3 x) + 3 x \cdot 4 + 4 (3 x + 4) - 36 - 15 x = 20$

Apply the distributive property.

$3 x (3 x) + 3 x \cdot 4 + 4 (3 x) + 4 \cdot 4 - 36 - 15 x = 20$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$3 \cdot 3 x \cdot x + 3 x \cdot 4 + 4 (3 x) + 4 \cdot 4 - 36 - 15 x = 20$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$3 \cdot 3 (x \cdot x) + 3 x \cdot 4 + 4 (3 x) + 4 \cdot 4 - 36 - 15 x = 20$

Multiply $x$ by $x$ .

$3 \cdot 3 x^{2} + 3 x \cdot 4 + 4 (3 x) + 4 \cdot 4 - 36 - 15 x = 20$

Multiply $3$ by $3$ .

$9 x^{2} + 3 x \cdot 4 + 4 (3 x) + 4 \cdot 4 - 36 - 15 x = 20$

Multiply $4$ by $3$ .

$9 x^{2} + 12 x + 4 (3 x) + 4 \cdot 4 - 36 - 15 x = 20$

Multiply $3$ by $4$ .

$9 x^{2} + 12 x + 12 x + 4 \cdot 4 - 36 - 15 x = 20$

Multiply $4$ by $4$ .

$9 x^{2} + 12 x + 12 x + 16 - 36 - 15 x = 20$

Add $12 x$ and $12 x$ .

$9 x^{2} + 24 x + 16 - 36 - 15 x = 20$

Subtract $15 x$ from $24 x$ .

$9 x^{2} + 9 x + 16 - 36 = 20$

Subtract $36$ from $16$ .

$9 x^{2} + 9 x - 20 = 20$

Subtract $20$ from both sides of the equation.

$9 x^{2} + 9 x - 20 - 20 = 0$

Subtract $20$ from $- 20$ .

$9 x^{2} + 9 x - 40 = 0$

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 $a \cdot c = 9 \cdot - 40 = - 360$ and whose sum is $b = 9$ .

Factor $9$ out of $9 x$ .

$9 x^{2} + 9 (x) - 40 = 0$

Rewrite $9$ as $- 15$ plus $24$

$9 x^{2} + (- 15 + 24) x - 40 = 0$

Apply the distributive property.

$9 x^{2} - 15 x + 24 x - 40 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(9 x^{2} - 15 x) + 24 x - 40 = 0$

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

$3 x (3 x - 5) + 8 (3 x - 5) = 0$

Factor the polynomial by factoring out the greatest common factor, $3 x - 5$ .

$(3 x - 5) (3 x + 8) = 0$

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

$3 x - 5 = 0$

$3 x + 8 = 0$

Set $3 x - 5$ equal to $0$ and solve for $x$ .

Set $3 x - 5$ equal to $0$ .

$3 x - 5 = 0$

Solve $3 x - 5 = 0$ for $x$ .

Add $5$ to both sides of the equation.

$3 x = 5$

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

Divide each term in $3 x = 5$ by $3$ .

$\frac{3 x}{3} = \frac{5}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{5}{3}$

Divide $x$ by $1$ .

$x = \frac{5}{3}$

Set $3 x + 8$ equal to $0$ and solve for $x$ .

Set $3 x + 8$ equal to $0$ .

$3 x + 8 = 0$

Solve $3 x + 8 = 0$ for $x$ .

Subtract $8$ from both sides of the equation.

$3 x = - 8$

Divide each term in $3 x = - 8$ by $3$ and simplify.

Divide each term in $3 x = - 8$ by $3$ .

$\frac{3 x}{3} = \frac{- 8}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 8}{3}$

Divide $x$ by $1$ .

$x = \frac{- 8}{3}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{8}{3}$

The final solution is all the values that make $(3 x - 5) (3 x + 8) = 0$ true.

$x = \frac{5}{3}, - \frac{8}{3}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{5}{3}, - \frac{8}{3}$

Decimal Form:

$x = 1.\overline{6}, - 2.\overline{6}$

Mixed Number Form:

$x = 1 \frac{2}{3}, - 2 \frac{2}{3}$

Solve for x (3x+4)^2-36=15x+20

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