Solve (x^2-4)(x^2-25)/(x+2)(x+5=0

$$\frac { ( x ^ { 2 } - 4 ) ( x ^ { 2 } - 25 ) } { ( x + 2 ) ( x + 5 } = 0$$

Solve for x

$$x=5$$

$$x=2$$

Steps Using the Quadratic Formula

Variable x cannot be equal to any of the values -5,-2 since division by zero is not defined. Multiply both sides of the equation by \left(x+2\right)\left(x+5\right).

$$\left(x^{2}-4\right)\left(x^{2}-25\right)=0$$

Use the distributive property to multiply x^{2}-4 by x^{2}-25 and combine like terms.

$$x^{4}-29x^{2}+100=0$$

Substitute t for x^{2}.

$$t^{2}-29t+100=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Substitute 1 for a, -29 for b, and 100 for c in the quadratic formula.

$$t=\frac{-\left(-29\right)±\sqrt{\left(-29\right)^{2}-4\times 1\times 100}}{2}$$

Do the calculations.

$$t=\frac{29±21}{2}$$

Solve the equation t=\frac{29±21}{2} when ± is plus and when ± is minus.

$$t=25 t=4$$

Since x=t^{2}, the solutions are obtained by evaluating x=±\sqrt{t} for each t.

$$x=5 x=-5 x=2 x=-2$$

Variable x cannot be equal to any of the values -5,-2.

$$x=2 x=5$$