(x-3)2+7(x-3)+6=0

Solution for (x-3)2+7(x-3)+6=0 equation:

Simplifying
(x + -3) * 2 + 7(x + -3) + 6 = 0

Reorder the terms:
(-3 + x) * 2 + 7(x + -3) + 6 = 0

Reorder the terms for easier multiplication:
2(-3 + x) + 7(x + -3) + 6 = 0
(-3 * 2 + x * 2) + 7(x + -3) + 6 = 0
(-6 + 2x) + 7(x + -3) + 6 = 0

Reorder the terms:
-6 + 2x + 7(-3 + x) + 6 = 0
-6 + 2x + (-3 * 7 + x * 7) + 6 = 0
-6 + 2x + (-21 + 7x) + 6 = 0

Reorder the terms:
-6 + -21 + 6 + 2x + 7x = 0

Combine like terms: -6 + -21 = -27
-27 + 6 + 2x + 7x = 0

Combine like terms: -27 + 6 = -21
-21 + 2x + 7x = 0

Combine like terms: 2x + 7x = 9x
-21 + 9x = 0

Solving
-21 + 9x = 0

Solving for variable 'x'.

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

Add '21' to each side of the equation.
-21 + 21 + 9x = 0 + 21

Combine like terms: -21 + 21 = 0
0 + 9x = 0 + 21
9x = 0 + 21

Combine like terms: 0 + 21 = 21
9x = 21

Divide each side by '9'.
x = 2.333333333

Simplifying
x = 2.333333333