78=x(2x+1)

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

Simplifying
78 = x(2x + 1)

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

Solving
78 = 1x + 2x2

Solving for variable 'x'.

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

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

Combine like terms: 2x2 + -2x2 = 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}