(4x+2)x=72

Solution for (4x+2)x=72 equation:

Simplifying
(4x + 2) * x = 72

Reorder the terms:
(2 + 4x) * x = 72

Reorder the terms for easier multiplication:
x(2 + 4x) = 72
(2 * x + 4x * x) = 72
(2x + 4x2) = 72

Solving
2x + 4x2 = 72

Solving for variable 'x'.

Reorder the terms:
-72 + 2x + 4x2 = 72 + -72

Combine like terms: 72 + -72 = 0
-72 + 2x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-36 + x + 2x2) = 0

Factor a trinomial.
2((-9 + -2x)(4 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-9 + -2x)' equal to zero and attempt to solve:

Simplifying
-9 + -2x = 0

Solving
-9 + -2x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -2x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2x = 0 + 9
-2x = 0 + 9

Combine like terms: 0 + 9 = 9
-2x = 9

Divide each side by '-2'.
x = -4.5

Simplifying
x = -4.5
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 = {-4.5, 4}