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

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


Simplifying
4x(x + 2) = 4(x + 6)

Reorder the terms:
4x(2 + x) = 4(x + 6)
(2 * 4x + x * 4x) = 4(x + 6)
(8x + 4x2) = 4(x + 6)

Reorder the terms:
8x + 4x2 = 4(6 + x)
8x + 4x2 = (6 * 4 + x * 4)
8x + 4x2 = (24 + 4x)

Solving
8x + 4x2 = 24 + 4x

Solving for variable 'x'.

Reorder the terms:
-24 + 8x + -4x + 4x2 = 24 + 4x + -24 + -4x

Combine like terms: 8x + -4x = 4x
-24 + 4x + 4x2 = 24 + 4x + -24 + -4x

Reorder the terms:
-24 + 4x + 4x2 = 24 + -24 + 4x + -4x

Combine like terms: 24 + -24 = 0
-24 + 4x + 4x2 = 0 + 4x + -4x
-24 + 4x + 4x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-24 + 4x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-6 + x + x2) = 0

Factor a trinomial.
4((-3 + -1x)(2 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-3, 2}

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