0.5(4x+4)(x+1)=50

Solution for 0.5(4x+4)(x+1)=50 equation:

Simplifying
0.5(4x + 4)(x + 1) = 50

Reorder the terms:
0.5(4 + 4x)(x + 1) = 50

Reorder the terms:
0.5(4 + 4x)(1 + x) = 50

Multiply (4 + 4x) * (1 + x)
0.5(4(1 + x) + 4x * (1 + x)) = 50
0.5((1 * 4 + x * 4) + 4x * (1 + x)) = 50
0.5((4 + 4x) + 4x * (1 + x)) = 50
0.5(4 + 4x + (1 * 4x + x * 4x)) = 50
0.5(4 + 4x + (4x + 4x2)) = 50

Combine like terms: 4x + 4x = 8x
0.5(4 + 8x + 4x2) = 50
(4 * 0.5 + 8x * 0.5 + 4x2 * 0.5) = 50
(2 + 4x + 2x2) = 50

Solving
2 + 4x + 2x2 = 50

Solving for variable 'x'.

Reorder the terms:
2 + -50 + 4x + 2x2 = 50 + -50

Combine like terms: 2 + -50 = -48
-48 + 4x + 2x2 = 50 + -50

Combine like terms: 50 + -50 = 0
-48 + 4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-24 + 2x + x2) = 0

Factor a trinomial.
2((-6 + -1x)(4 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-6, 4}