2x[7+6x(5+4)]=122

Solution for 2x[7+6x(5+4)]=122 equation:

Simplifying
2x[7 + 6x(5 + 4)] = 122

Combine like terms: 5 + 4 = 9
2x[7 + 6x(9)] = 122

Reorder the terms for easier multiplication:
2x[7 + 6 * 9x] = 122

Multiply 6 * 9
2x[7 + 54x] = 122
[7 * 2x + 54x * 2x] = 122
[14x + 108x2] = 122

Solving
14x + 108x2 = 122

Solving for variable 'x'.

Reorder the terms:
-122 + 14x + 108x2 = 122 + -122

Combine like terms: 122 + -122 = 0
-122 + 14x + 108x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-61 + 7x + 54x2) = 0

Factor a trinomial.
2((-61 + -54x)(1 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-61 + -54x)' equal to zero and attempt to solve:

Simplifying
-61 + -54x = 0

Solving
-61 + -54x = 0

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

Add '61' to each side of the equation.
-61 + 61 + -54x = 0 + 61

Combine like terms: -61 + 61 = 0
0 + -54x = 0 + 61
-54x = 0 + 61

Combine like terms: 0 + 61 = 61
-54x = 61

Divide each side by '-54'.
x = -1.12962963

Simplifying
x = -1.12962963
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {-1.12962963, 1}