-40+2n=4n-8(n+8) — step-by-step solution

Let's solve in

ℝ

- 40 + 2 n = 4 n - 8 \cdot (n + 8)

ⓘ Expand by multiplying each term inside the parentheses:

- 8 \cdot (n + 8)

- (8 n + 64)

- 40 + 2 n = 4 n - (8 n + 64)

ⓘ A minus sign before a parenthesis changes the sign of each of its terms:

- (8 n + 64)

- 8 n - 64

- 40 + 2 n = 4 n - 8 n - 64

ⓘ Like terms are grouped by adding their coefficients:

4 n - 8 n

-4 n

- 40 + 2 n = - 4 n - 64

ⓘ We add

40

to both sides■Start from

-64

and move forward

40

on the number line, getting closer to zero:

- 64 + 40

-24

2 n = - 4 n - 24

ⓘ We add

4 n

to both sides

2 n + 4 n = -24

ⓘ Like terms are grouped by adding their coefficients:

2 n + 4 n

6 n

6 n = -24

ⓘ Both sides are divided by

6

n = - \frac{24}{6}

ⓘ We simplify the fraction by dividing the numerator and the denominator by

6

, their greatest common divisor:

- \frac{24}{6}

-4

▶Solution found:

n = -4