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

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

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

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

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

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

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

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

Combine like terms: -1x + x = 0
-12 + 0 + x2 = 52
-12 + x2 = 52

Solving
-12 + x2 = 52

Solving for variable 'x'.

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

Add '12' to each side of the equation.
-12 + 12 + x2 = 52 + 12

Combine like terms: -12 + 12 = 0
0 + x2 = 52 + 12
x2 = 52 + 12

Combine like terms: 52 + 12 = 64
x2 = 64

Simplifying
x2 = 64

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