(x+3)(2x-26)=0

Solution for (x+3)(2x-26)=0 equation:

Simplifying
(x + 3)(2x + -26) = 0

Reorder the terms:
(3 + x)(2x + -26) = 0

Reorder the terms:
(3 + x)(-26 + 2x) = 0

Multiply (3 + x) * (-26 + 2x)
(3(-26 + 2x) + x(-26 + 2x)) = 0
((-26 * 3 + 2x * 3) + x(-26 + 2x)) = 0
((-78 + 6x) + x(-26 + 2x)) = 0
(-78 + 6x + (-26 * x + 2x * x)) = 0
(-78 + 6x + (-26x + 2x2)) = 0

Combine like terms: 6x + -26x = -20x
(-78 + -20x + 2x2) = 0

Solving
-78 + -20x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-39 + -10x + x2) = 0

Factor a trinomial.
2((-3 + -1x)(13 + -1x)) = 0

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

Simplifying
13 + -1x = 0

Solving
13 + -1x = 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 + -1x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1x = 0 + -13
-1x = 0 + -13

Combine like terms: 0 + -13 = -13
-1x = -13

Divide each side by '-1'.
x = 13

Simplifying
x = 13
Solution
x = {-3, 13}