(x+13)(-2x+2)+24x=0

Solution for (x+13)(-2x+2)+24x=0 equation:

Simplifying
(x + 13)(-2x + 2) + 24x = 0

Reorder the terms:
(13 + x)(-2x + 2) + 24x = 0

Reorder the terms:
(13 + x)(2 + -2x) + 24x = 0

Multiply (13 + x) * (2 + -2x)
(13(2 + -2x) + x(2 + -2x)) + 24x = 0
((2 * 13 + -2x * 13) + x(2 + -2x)) + 24x = 0
((26 + -26x) + x(2 + -2x)) + 24x = 0
(26 + -26x + (2 * x + -2x * x)) + 24x = 0
(26 + -26x + (2x + -2x2)) + 24x = 0

Combine like terms: -26x + 2x = -24x
(26 + -24x + -2x2) + 24x = 0

Reorder the terms:
26 + -24x + 24x + -2x2 = 0

Combine like terms: -24x + 24x = 0
26 + 0 + -2x2 = 0
26 + -2x2 = 0

Solving
26 + -2x2 = 0

Solving for variable 'x'.

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

Add '-26' to each side of the equation.
26 + -26 + -2x2 = 0 + -26

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

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

Divide each side by '-2'.
x2 = 13

Simplifying
x2 = 13

Take the square root of each side:
x = {-3.605551275, 3.605551275}