x(2x-26)=-72

Solution for x(2x-26)=-72 equation:

Simplifying
x(2x + -26) = -72

Reorder the terms:
x(-26 + 2x) = -72
(-26 * x + 2x * x) = -72
(-26x + 2x2) = -72

Solving
-26x + 2x2 = -72

Solving for variable 'x'.

Reorder the terms:
72 + -26x + 2x2 = -72 + 72

Combine like terms: -72 + 72 = 0
72 + -26x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(36 + -13x + x2) = 0

Factor a trinomial.
2((4 + -1x)(9 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {4, 9}