Solve for x x^2=(x+6)(x-6)+36

$x^{2} = (x + 6) (x - 6) + 36$

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$(x + 6) (x - 6) + 36 = x^{2}$

Simplify $(x + 6) (x - 6) + 36$ .

Simplify each term.

Expand $(x + 6) (x - 6)$ using the FOIL Method.

Apply the distributive property.

$x (x - 6) + 6 (x - 6) + 36 = x^{2}$

Apply the distributive property.

$x \cdot x + x \cdot - 6 + 6 (x - 6) + 36 = x^{2}$

Apply the distributive property.

$x \cdot x + x \cdot - 6 + 6 x + 6 \cdot - 6 + 36 = x^{2}$

Combine the opposite terms in $x \cdot x + x \cdot - 6 + 6 x + 6 \cdot - 6$ .

Reorder the factors in the terms $x \cdot - 6$ and $6 x$ .

$x \cdot x - 6 x + 6 x + 6 \cdot - 6 + 36 = x^{2}$

Add $- 6 x$ and $6 x$ .

$x \cdot x + 0 + 6 \cdot - 6 + 36 = x^{2}$

Add $x \cdot x$ and $0$ .

$x \cdot x + 6 \cdot - 6 + 36 = x^{2}$

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + 6 \cdot - 6 + 36 = x^{2}$

Multiply $6$ by $- 6$ .

$x^{2} - 36 + 36 = x^{2}$

Combine the opposite terms in $x^{2} - 36 + 36$ .

Add $- 36$ and $36$ .

$x^{2} + 0 = x^{2}$

Add $x^{2}$ and $0$ .

$x^{2} = x^{2}$

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

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

$x^{2} - x^{2} = 0$

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

$0 = 0$

Since $0 = 0$ , the equation will always be true for any value of $x$ .

All real numbers

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$