4(x+3)=2x(2x+6)

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Solution for 4(x+3)=2x(2x+6) equation: 


Simplifying
4(x + 3) = 2x(2x + 6)

Reorder the terms:
4(3 + x) = 2x(2x + 6)
(3 * 4 + x * 4) = 2x(2x + 6)
(12 + 4x) = 2x(2x + 6)

Reorder the terms:
12 + 4x = 2x(6 + 2x)
12 + 4x = (6 * 2x + 2x * 2x)
12 + 4x = (12x + 4x2)

Solving
12 + 4x = 12x + 4x2

Solving for variable 'x'.

Combine like terms: 4x + -12x = -8x
12 + -8x + -4x2 = 12x + 4x2 + -12x + -4x2

Reorder the terms:
12 + -8x + -4x2 = 12x + -12x + 4x2 + -4x2

Combine like terms: 12x + -12x = 0
12 + -8x + -4x2 = 0 + 4x2 + -4x2
12 + -8x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
12 + -8x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(3 + -2x + -1x2) = 0

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

Ignore the factor 4.

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 '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

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

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

Simplifying
x = -3
Solution
x = {1, -3}

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