4x+32=4x(11-2x)

Solution for 4x+32=4x(11-2x) equation:

Simplifying
4x + 32 = 4x(11 + -2x)

Reorder the terms:
32 + 4x = 4x(11 + -2x)
32 + 4x = (11 * 4x + -2x * 4x)
32 + 4x = (44x + -8x2)

Solving
32 + 4x = 44x + -8x2

Solving for variable 'x'.

Combine like terms: 4x + -44x = -40x
32 + -40x + 8x2 = 44x + -8x2 + -44x + 8x2

Reorder the terms:
32 + -40x + 8x2 = 44x + -44x + -8x2 + 8x2

Combine like terms: 44x + -44x = 0
32 + -40x + 8x2 = 0 + -8x2 + 8x2
32 + -40x + 8x2 = -8x2 + 8x2

Combine like terms: -8x2 + 8x2 = 0
32 + -40x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(4 + -5x + x2) = 0

Factor a trinomial.
8((1 + -1x)(4 + -1x)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
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 = {1, 4}