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

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

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

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

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

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

Combine like terms: -2x + 3x = 1x
(-2 + 1x + 3x2) = 3(x + 4)(x + -1)

Reorder the terms:
-2 + 1x + 3x2 = 3(4 + x)(x + -1)

Reorder the terms:
-2 + 1x + 3x2 = 3(4 + x)(-1 + x)

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

Combine like terms: 4x + -1x = 3x
-2 + 1x + 3x2 = 3(-4 + 3x + x2)
-2 + 1x + 3x2 = (-4 * 3 + 3x * 3 + x2 * 3)
-2 + 1x + 3x2 = (-12 + 9x + 3x2)

Add '-3x2' to each side of the equation.
-2 + 1x + 3x2 + -3x2 = -12 + 9x + 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-2 + 1x + 0 = -12 + 9x + 3x2 + -3x2
-2 + 1x = -12 + 9x + 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-2 + 1x = -12 + 9x + 0
-2 + 1x = -12 + 9x

Solving
-2 + 1x = -12 + 9x

Solving for variable 'x'.

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

Add '-9x' to each side of the equation.
-2 + 1x + -9x = -12 + 9x + -9x

Combine like terms: 1x + -9x = -8x
-2 + -8x = -12 + 9x + -9x

Combine like terms: 9x + -9x = 0
-2 + -8x = -12 + 0
-2 + -8x = -12

Add '2' to each side of the equation.
-2 + 2 + -8x = -12 + 2

Combine like terms: -2 + 2 = 0
0 + -8x = -12 + 2
-8x = -12 + 2

Combine like terms: -12 + 2 = -10
-8x = -10

Divide each side by '-8'.
x = 1.25

Simplifying
x = 1.25