(3x-5)x=78

Solution for (3x-5)x=78 equation:

Simplifying
(3x + -5) * x = 78

Reorder the terms:
(-5 + 3x) * x = 78

Reorder the terms for easier multiplication:
x(-5 + 3x) = 78
(-5 * x + 3x * x) = 78
(-5x + 3x2) = 78

Solving
-5x + 3x2 = 78

Solving for variable 'x'.

Reorder the terms:
-78 + -5x + 3x2 = 78 + -78

Combine like terms: 78 + -78 = 0
-78 + -5x + 3x2 = 0

Factor a trinomial.
(-13 + -3x)(6 + -1x) = 0

Subproblem 1
Set the factor '(-13 + -3x)' equal to zero and attempt to solve:

Simplifying
-13 + -3x = 0

Solving
-13 + -3x = 0

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

Add '13' to each side of the equation.
-13 + 13 + -3x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -3x = 0 + 13
-3x = 0 + 13

Combine like terms: 0 + 13 = 13
-3x = 13

Divide each side by '-3'.
x = -4.333333333

Simplifying
x = -4.333333333
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-4.333333333, 6}