Evaluate z1z2, given that z1 = 2 − 3i and z2 = 5 + 7i.

Discriminant: $b^{2} - 4ac = (-4)^{2} - 4(1)(-3) = 16 + 12 = 28$.

x = 2 \pm \sqrt{7}

$x - 2 = 0 \quad \Rightarrow \quad x = 2$
$x - 3 = 0 \quad \Rightarrow \quad x = 3$
x=2 \quad or \quad x=3

$2x - 1 = 0 \quad \Rightarrow \quad x = \dfrac{1}{2}$
$x + 3 = 0 \quad \Rightarrow \quad x = -3$
x = \dfrac{1}{2} \quad or \quad x = -3

Divide leading terms: $\dfrac{x^{2}}{x} = x$.
Multiply: $x(x - 2) = x^{2} - 2x$.
Subtract: $(x^{2} - 4) - (x^{2} - 2x) = 2x - 4$.

$\dfrac{2x}{x} = 2$.
Multiply: $2(x - 2) = 2x - 4$.
Subtract: $(2x - 4) - (2x - 4) = 0$.
Quotient is $x + 2$, remainder 0.
x + 2

x = -2

x = \pm 2

$x - 5 = 0 \quad \Rightarrow \quad x = 5$
$x + 1 = 0 \quad \Rightarrow \quad x = -1$
x = 5 \quad or \quad x = -1

$2x = 0 \quad \Rightarrow \quad x = 0$
$x - 4 = 0 \quad \Rightarrow \quad x = 4$
x = 0 \quad or \quad x = 4

$x - 4 = 0 \quad \Rightarrow \quad x = 4$
$x - 2 = 0 \quad \Rightarrow \quad x = 2$
x = 4 \quad or \quad x = 2

x = -\dfrac{3}{2}

$x + 3 = 0 \quad \Rightarrow \quad x = -3$
$x - 1 = 0 \quad \Rightarrow \quad x = 1$
x = -3 \quad or \quad x = 1