6(x+2)(2x-3)=4(3x-1)(x+1)

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Solution for 6(x+2)(2x-3)=4(3x-1)(x+1) equation: 


Simplifying
6(x + 2)(2x + -3) = 4(3x + -1)(x + 1)

Reorder the terms:
6(2 + x)(2x + -3) = 4(3x + -1)(x + 1)

Reorder the terms:
6(2 + x)(-3 + 2x) = 4(3x + -1)(x + 1)

Multiply (2 + x) * (-3 + 2x)
6(2(-3 + 2x) + x(-3 + 2x)) = 4(3x + -1)(x + 1)
6((-3 * 2 + 2x * 2) + x(-3 + 2x)) = 4(3x + -1)(x + 1)
6((-6 + 4x) + x(-3 + 2x)) = 4(3x + -1)(x + 1)
6(-6 + 4x + (-3 * x + 2x * x)) = 4(3x + -1)(x + 1)
6(-6 + 4x + (-3x + 2x2)) = 4(3x + -1)(x + 1)

Combine like terms: 4x + -3x = 1x
6(-6 + 1x + 2x2) = 4(3x + -1)(x + 1)
(-6 * 6 + 1x * 6 + 2x2 * 6) = 4(3x + -1)(x + 1)
(-36 + 6x + 12x2) = 4(3x + -1)(x + 1)

Reorder the terms:
-36 + 6x + 12x2 = 4(-1 + 3x)(x + 1)

Reorder the terms:
-36 + 6x + 12x2 = 4(-1 + 3x)(1 + x)

Multiply (-1 + 3x) * (1 + x)
-36 + 6x + 12x2 = 4(-1(1 + x) + 3x * (1 + x))
-36 + 6x + 12x2 = 4((1 * -1 + x * -1) + 3x * (1 + x))
-36 + 6x + 12x2 = 4((-1 + -1x) + 3x * (1 + x))
-36 + 6x + 12x2 = 4(-1 + -1x + (1 * 3x + x * 3x))
-36 + 6x + 12x2 = 4(-1 + -1x + (3x + 3x2))

Combine like terms: -1x + 3x = 2x
-36 + 6x + 12x2 = 4(-1 + 2x + 3x2)
-36 + 6x + 12x2 = (-1 * 4 + 2x * 4 + 3x2 * 4)
-36 + 6x + 12x2 = (-4 + 8x + 12x2)

Add '-12x2' to each side of the equation.
-36 + 6x + 12x2 + -12x2 = -4 + 8x + 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
-36 + 6x + 0 = -4 + 8x + 12x2 + -12x2
-36 + 6x = -4 + 8x + 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
-36 + 6x = -4 + 8x + 0
-36 + 6x = -4 + 8x

Solving
-36 + 6x = -4 + 8x

Solving for variable 'x'.

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

Add '-8x' to each side of the equation.
-36 + 6x + -8x = -4 + 8x + -8x

Combine like terms: 6x + -8x = -2x
-36 + -2x = -4 + 8x + -8x

Combine like terms: 8x + -8x = 0
-36 + -2x = -4 + 0
-36 + -2x = -4

Add '36' to each side of the equation.
-36 + 36 + -2x = -4 + 36

Combine like terms: -36 + 36 = 0
0 + -2x = -4 + 36
-2x = -4 + 36

Combine like terms: -4 + 36 = 32
-2x = 32

Divide each side by '-2'.
x = -16

Simplifying
x = -16

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