Left parenthesis, minus, x, cubed, minus, x, right parenthesis, plus, left parenthesis, 6, x, squared, plus, 6, x, minus, 7, right parenthesis, equals

(-x³ - x) + (6x² + 6x - 7)

= -x³ + 6x² + 5x - 7

Step-by-step explanation:

Given the function:

(-x³ - x) + (6x² + 6x - 7)

This can be simplified to

-x³ - x + 6x² + 6x - 7

Collecting like terms, we have

-x³ + 6x² - x + 6x - 7

= -x³ + 6x² + 5x - 7

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .