Solve for x (x+7)(x-4)=x^2+9x-28

$(x + 7) (x - 4) = x^{2} + 9 x - 28$

Step 1

Simplify $(x + 7) (x - 4)$ .

Rewrite.

$0 + 0 + (x + 7) (x - 4) = x^{2} + 9 x - 28$

Simplify by adding zeros.

$(x + 7) (x - 4) = x^{2} + 9 x - 28$

Expand $(x + 7) (x - 4)$ using the FOIL Method.

Apply the distributive property.

$x (x - 4) + 7 (x - 4) = x^{2} + 9 x - 28$

Apply the distributive property.

$x \cdot x + x \cdot - 4 + 7 (x - 4) = x^{2} + 9 x - 28$

Apply the distributive property.

$x \cdot x + x \cdot - 4 + 7 x + 7 \cdot - 4 = x^{2} + 9 x - 28$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 4 + 7 x + 7 \cdot - 4 = x^{2} + 9 x - 28$

Move $- 4$ to the left of $x$ .

$x^{2} - 4 \cdot x + 7 x + 7 \cdot - 4 = x^{2} + 9 x - 28$

Multiply $7$ by $- 4$ .

$x^{2} - 4 x + 7 x - 28 = x^{2} + 9 x - 28$

Add $- 4 x$ and $7 x$ .

$x^{2} + 3 x - 28 = x^{2} + 9 x - 28$

Step 2

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

Subtract $x^{2}$ from both sides of the equation.

$x^{2} + 3 x - 28 - x^{2} = 9 x - 28$

Subtract $9 x$ from both sides of the equation.

$x^{2} + 3 x - 28 - x^{2} - 9 x = - 28$

Combine the opposite terms in $x^{2} + 3 x - 28 - x^{2} - 9 x$ .

Subtract $x^{2}$ from $x^{2}$ .

$3 x - 28 + 0 - 9 x = - 28$

Add $3 x - 28$ and $0$ .

$3 x - 28 - 9 x = - 28$

Subtract $9 x$ from $3 x$ .

$- 6 x - 28 = - 28$

Step 3

Move all terms not containing $x$ to the right side of the equation.

Add $28$ to both sides of the equation.

$- 6 x = - 28 + 28$

Add $- 28$ and $28$ .

$- 6 x = 0$

Step 4

Divide each term in $- 6 x = 0$ by $- 6$ and simplify.

Divide each term in $- 6 x = 0$ by $- 6$ .

$\frac{- 6 x}{- 6} = \frac{0}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 x}{- 6} = \frac{0}{- 6}$

Divide $x$ by $1$ .

$x = \frac{0}{- 6}$

Simplify the right side.

Divide $0$ by $- 6$ .

$x = 0$

Solve for x (x+7)(x-4)=x^2+9x-28

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