(3+2x)x=77

Solution for (3+2x)x=77 equation:

Simplifying
(3 + 2x) * x = 77

Reorder the terms for easier multiplication:
x(3 + 2x) = 77
(3 * x + 2x * x) = 77
(3x + 2x2) = 77

Solving
3x + 2x2 = 77

Solving for variable 'x'.

Reorder the terms:
-77 + 3x + 2x2 = 77 + -77

Combine like terms: 77 + -77 = 0
-77 + 3x + 2x2 = 0

Factor a trinomial.
(-7 + -1x)(11 + -2x) = 0

Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7
Subproblem 2
Set the factor '(11 + -2x)' equal to zero and attempt to solve:

Simplifying
11 + -2x = 0

Solving
11 + -2x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -2x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -2x = 0 + -11
-2x = 0 + -11

Combine like terms: 0 + -11 = -11
-2x = -11

Divide each side by '-2'.
x = 5.5

Simplifying
x = 5.5
Solution
x = {-7, 5.5}