(x+3)(x-4)-52=-x

Solution for (x+3)(x-4)-52=-x equation:

Simplifying
(x + 3)(x + -4) + -52 = -1x

Reorder the terms:
(3 + x)(x + -4) + -52 = -1x

Reorder the terms:
(3 + x)(-4 + x) + -52 = -1x

Multiply (3 + x) * (-4 + x)
(3(-4 + x) + x(-4 + x)) + -52 = -1x
((-4 * 3 + x * 3) + x(-4 + x)) + -52 = -1x
((-12 + 3x) + x(-4 + x)) + -52 = -1x
(-12 + 3x + (-4 * x + x * x)) + -52 = -1x
(-12 + 3x + (-4x + x2)) + -52 = -1x

Combine like terms: 3x + -4x = -1x
(-12 + -1x + x2) + -52 = -1x

Reorder the terms:
-12 + -52 + -1x + x2 = -1x

Combine like terms: -12 + -52 = -64
-64 + -1x + x2 = -1x

Add 'x' to each side of the equation.
-64 + -1x + x + x2 = -1x + x

Combine like terms: -1x + x = 0
-64 + 0 + x2 = -1x + x
-64 + x2 = -1x + x

Combine like terms: -1x + x = 0
-64 + x2 = 0

Solving
-64 + x2 = 0

Solving for variable 'x'.

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

Add '64' to each side of the equation.
-64 + 64 + x2 = 0 + 64

Combine like terms: -64 + 64 = 0
0 + x2 = 0 + 64
x2 = 0 + 64

Combine like terms: 0 + 64 = 64
x2 = 64

Simplifying
x2 = 64

Take the square root of each side:
x = {-8, 8}