(4+2x)(3+2x)=12

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Solution for (4+2x)(3+2x)=12 equation: 


Simplifying
(4 + 2x)(3 + 2x) = 12

Multiply (4 + 2x) * (3 + 2x)
(4(3 + 2x) + 2x * (3 + 2x)) = 12
((3 * 4 + 2x * 4) + 2x * (3 + 2x)) = 12
((12 + 8x) + 2x * (3 + 2x)) = 12
(12 + 8x + (3 * 2x + 2x * 2x)) = 12
(12 + 8x + (6x + 4x2)) = 12

Combine like terms: 8x + 6x = 14x
(12 + 14x + 4x2) = 12

Add '-12' to each side of the equation.
12 + 14x + -12 + 4x2 = 12 + -12

Reorder the terms:
12 + -12 + 14x + 4x2 = 12 + -12

Combine like terms: 12 + -12 = 0
0 + 14x + 4x2 = 12 + -12
14x + 4x2 = 12 + -12

Combine like terms: 12 + -12 = 0
14x + 4x2 = 0

Solving
14x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(7 + 2x) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(7 + 2x)' equal to zero and attempt to solve:

Simplifying
7 + 2x = 0

Solving
7 + 2x = 0

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

Add '-7' to each side of the equation.
7 + -7 + 2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2x = 0 + -7
2x = 0 + -7

Combine like terms: 0 + -7 = -7
2x = -7

Divide each side by '2'.
x = -3.5

Simplifying
x = -3.5
Solution
x = {0, -3.5}

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