2(4+x)+6(5+x)=x(x+8)

Solution for 2(4+x)+6(5+x)=x(x+8) equation:

Simplifying
2(4 + x) + 6(5 + x) = x(x + 8)
(4 * 2 + x * 2) + 6(5 + x) = x(x + 8)
(8 + 2x) + 6(5 + x) = x(x + 8)
8 + 2x + (5 * 6 + x * 6) = x(x + 8)
8 + 2x + (30 + 6x) = x(x + 8)

Reorder the terms:
8 + 30 + 2x + 6x = x(x + 8)

Combine like terms: 8 + 30 = 38
38 + 2x + 6x = x(x + 8)

Combine like terms: 2x + 6x = 8x
38 + 8x = x(x + 8)

Reorder the terms:
38 + 8x = x(8 + x)
38 + 8x = (8 * x + x * x)
38 + 8x = (8x + x2)

Add '-8x' to each side of the equation.
38 + 8x + -8x = 8x + -8x + x2

Combine like terms: 8x + -8x = 0
38 + 0 = 8x + -8x + x2
38 = 8x + -8x + x2

Combine like terms: 8x + -8x = 0
38 = 0 + x2
38 = x2

Solving
38 = x2

Solving for variable 'x'.

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

Add '-1x2' to each side of the equation.
38 + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
38 + -1x2 = 0

Add '-38' to each side of the equation.
38 + -38 + -1x2 = 0 + -38

Combine like terms: 38 + -38 = 0
0 + -1x2 = 0 + -38
-1x2 = 0 + -38

Combine like terms: 0 + -38 = -38
-1x2 = -38

Divide each side by '-1'.
x2 = 38

Simplifying
x2 = 38

Take the square root of each side:
x = {-6.164414003, 6.164414003}