(2x+4)(-3x+6)+12=3x^2

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Solution for (2x+4)(-3x+6)+12=3x^2 equation: 


Simplifying
(2x + 4)(-3x + 6) + 12 = 3x2

Reorder the terms:
(4 + 2x)(-3x + 6) + 12 = 3x2

Reorder the terms:
(4 + 2x)(6 + -3x) + 12 = 3x2

Multiply (4 + 2x) * (6 + -3x)
(4(6 + -3x) + 2x * (6 + -3x)) + 12 = 3x2
((6 * 4 + -3x * 4) + 2x * (6 + -3x)) + 12 = 3x2
((24 + -12x) + 2x * (6 + -3x)) + 12 = 3x2
(24 + -12x + (6 * 2x + -3x * 2x)) + 12 = 3x2
(24 + -12x + (12x + -6x2)) + 12 = 3x2

Combine like terms: -12x + 12x = 0
(24 + 0 + -6x2) + 12 = 3x2
(24 + -6x2) + 12 = 3x2

Reorder the terms:
24 + 12 + -6x2 = 3x2

Combine like terms: 24 + 12 = 36
36 + -6x2 = 3x2

Solving
36 + -6x2 = 3x2

Solving for variable 'x'.

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

Add '-3x2' to each side of the equation.
36 + -6x2 + -3x2 = 3x2 + -3x2

Combine like terms: -6x2 + -3x2 = -9x2
36 + -9x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
36 + -9x2 = 0

Add '-36' to each side of the equation.
36 + -36 + -9x2 = 0 + -36

Combine like terms: 36 + -36 = 0
0 + -9x2 = 0 + -36
-9x2 = 0 + -36

Combine like terms: 0 + -36 = -36
-9x2 = -36

Divide each side by '-9'.
x2 = 4

Simplifying
x2 = 4

Take the square root of each side:
x = {-2, 2}

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