x(2x-1)=78

Solution for x(2x-1)=78 equation:

Simplifying
x(2x + -1) = 78

Reorder the terms:
x(-1 + 2x) = 78
(-1 * x + 2x * x) = 78
(-1x + 2x2) = 78

Solving
-1x + 2x2 = 78

Solving for variable 'x'.

Reorder the terms:
-78 + -1x + 2x2 = 78 + -78

Combine like terms: 78 + -78 = 0
-78 + -1x + 2x2 = 0

Factor a trinomial.
(-6 + -1x)(13 + -2x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(13 + -2x)' equal to zero and attempt to solve:

Simplifying
13 + -2x = 0

Solving
13 + -2x = 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 + -2x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -2x = 0 + -13
-2x = 0 + -13

Combine like terms: 0 + -13 = -13
-2x = -13

Divide each side by '-2'.
x = 6.5

Simplifying
x = 6.5
Solution
x = {-6, 6.5}