(2x+6)(5x-13)=0

Solution for (2x+6)(5x-13)=0 equation:

Simplifying
(2x + 6)(5x + -13) = 0

Reorder the terms:
(6 + 2x)(5x + -13) = 0

Reorder the terms:
(6 + 2x)(-13 + 5x) = 0

Multiply (6 + 2x) * (-13 + 5x)
(6(-13 + 5x) + 2x * (-13 + 5x)) = 0
((-13 * 6 + 5x * 6) + 2x * (-13 + 5x)) = 0
((-78 + 30x) + 2x * (-13 + 5x)) = 0
(-78 + 30x + (-13 * 2x + 5x * 2x)) = 0
(-78 + 30x + (-26x + 10x2)) = 0

Combine like terms: 30x + -26x = 4x
(-78 + 4x + 10x2) = 0

Solving
-78 + 4x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-39 + 2x + 5x2) = 0

Factor a trinomial.
2((-3 + -1x)(13 + -5x)) = 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 + -5x)' equal to zero and attempt to solve:

Simplifying
13 + -5x = 0

Solving
13 + -5x = 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 + -5x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -5x = 0 + -13
-5x = 0 + -13

Combine like terms: 0 + -13 = -13
-5x = -13

Divide each side by '-5'.
x = 2.6

Simplifying
x = 2.6
Solution
x = {-3, 2.6}