x(8+2x)=(3x+12)

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Solution for x(8+2x)=(3x+12) equation: 


Simplifying
x(8 + 2x) = (3x + 12)
(8 * x + 2x * x) = (3x + 12)
(8x + 2x2) = (3x + 12)

Reorder the terms:
8x + 2x2 = (12 + 3x)

Remove parenthesis around (12 + 3x)
8x + 2x2 = 12 + 3x

Solving
8x + 2x2 = 12 + 3x

Solving for variable 'x'.

Reorder the terms:
-12 + 8x + -3x + 2x2 = 12 + 3x + -12 + -3x

Combine like terms: 8x + -3x = 5x
-12 + 5x + 2x2 = 12 + 3x + -12 + -3x

Reorder the terms:
-12 + 5x + 2x2 = 12 + -12 + 3x + -3x

Combine like terms: 12 + -12 = 0
-12 + 5x + 2x2 = 0 + 3x + -3x
-12 + 5x + 2x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-12 + 5x + 2x2 = 0

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


Subproblem 1
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

Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-4, 1.5}

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