3x*4x+5x=123

Solution for 3x*4x+5x=123 equation:

Simplifying
3x * 4x + 5x = 123

Reorder the terms for easier multiplication:
3 * 4x * x + 5x = 123

Multiply 3 * 4
12x * x + 5x = 123

Multiply x * x
12x2 + 5x = 123

Reorder the terms:
5x + 12x2 = 123

Solving
5x + 12x2 = 123

Solving for variable 'x'.

Reorder the terms:
-123 + 5x + 12x2 = 123 + -123

Combine like terms: 123 + -123 = 0
-123 + 5x + 12x2 = 0

Factor a trinomial.
(-41 + -12x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-41 + -12x)' equal to zero and attempt to solve:

Simplifying
-41 + -12x = 0

Solving
-41 + -12x = 0

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

Add '41' to each side of the equation.
-41 + 41 + -12x = 0 + 41

Combine like terms: -41 + 41 = 0
0 + -12x = 0 + 41
-12x = 0 + 41

Combine like terms: 0 + 41 = 41
-12x = 41

Divide each side by '-12'.
x = -3.416666667

Simplifying
x = -3.416666667
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-3.416666667, 3}