(y^2)/2 =2y — step-by-step solution

1) Let's solve in

ℝ

\frac{y^{2}}{2} = 2 y

2) Let's add fractions:

\frac{y^{2}}{2} - 2 y = 0

ⓘ To add fractions, put them over the same denominator, then add the numerators:

\frac{y^{2}}{2} - 2 y

\frac{y^{2} - 2 y \cdot 2}{2}

\frac{y^{2} - 2 y \cdot 2}{2} = 0

ⓘ Multiplications are done before additions and subtractions:

2 \cdot 2

4

\frac{y^{2} - 4 y}{2} = 0

ⓘ What the terms have in common is factored out, so that the fraction can be simplified:

\frac{y^{2} - 4 y}{2}

\frac{y \cdot (y - 4)}{2}

\frac{y \cdot (y - 4)}{2} = 0

Let's solve in

ℝ

y \cdot (y - 4) = 0

A product is zero if and only if one of its factors is zero: we solve each factor equal to 0

⇥2.1) Let's solve in

ℝ

y = 0

⇥Solution obtained:

y = 0

⇥2.2) Let's solve in

ℝ

y - 4 = 0

⇥Solution found:

y = 4

▶Solution:

y = {0, 4}