Evaluate: x=-5
x=3

Solve for x: $x=-5$
$x=3$

Subtract $90$ from both sides.

$$x^{2}+2x+75-90=0$$

Subtract $90$ from $75$ to get $-15$.

$$x^{2}+2x-15=0$$

To solve the equation, factor $x^{2}+2x-15$ using formula $x^{2}+\left(a+b\right)x+ab=\left(x+a\right)\left(x+b\right)$. To find $a$ and $b$, set up a system to be solved.

$$a+b=2$$ $$ab=-15$$

Since $ab$ is negative, $a$ and $b$ have the opposite signs. Since $a+b$ is positive, the positive number has greater absolute value than the negative. List all such integer pairs that give product $-15$.

$$-1,15$$ $$-3,5$$

Calculate the sum for each pair.

$$-1+15=14$$ $$-3+5=2$$

The solution is the pair that gives sum $2$.

$$a=-3$$ $$b=5$$

Rewrite factored expression $\left(x+a\right)\left(x+b\right)$ using the obtained values.

$$\left(x-3\right)\left(x+5\right)$$

To find equation solutions, solve $x-3=0$ and $x+5=0$.

$$x=3$$ $$x=-5$$