7(x+1)-5(3x-1)=4(3x-1)(x+1)

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Solution for 7(x+1)-5(3x-1)=4(3x-1)(x+1) equation: 


Simplifying
7(x + 1) + -5(3x + -1) = 4(3x + -1)(x + 1)

Reorder the terms:
7(1 + x) + -5(3x + -1) = 4(3x + -1)(x + 1)
(1 * 7 + x * 7) + -5(3x + -1) = 4(3x + -1)(x + 1)
(7 + 7x) + -5(3x + -1) = 4(3x + -1)(x + 1)

Reorder the terms:
7 + 7x + -5(-1 + 3x) = 4(3x + -1)(x + 1)
7 + 7x + (-1 * -5 + 3x * -5) = 4(3x + -1)(x + 1)
7 + 7x + (5 + -15x) = 4(3x + -1)(x + 1)

Reorder the terms:
7 + 5 + 7x + -15x = 4(3x + -1)(x + 1)

Combine like terms: 7 + 5 = 12
12 + 7x + -15x = 4(3x + -1)(x + 1)

Combine like terms: 7x + -15x = -8x
12 + -8x = 4(3x + -1)(x + 1)

Reorder the terms:
12 + -8x = 4(-1 + 3x)(x + 1)

Reorder the terms:
12 + -8x = 4(-1 + 3x)(1 + x)

Multiply (-1 + 3x) * (1 + x)
12 + -8x = 4(-1(1 + x) + 3x * (1 + x))
12 + -8x = 4((1 * -1 + x * -1) + 3x * (1 + x))
12 + -8x = 4((-1 + -1x) + 3x * (1 + x))
12 + -8x = 4(-1 + -1x + (1 * 3x + x * 3x))
12 + -8x = 4(-1 + -1x + (3x + 3x2))

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

Solving
12 + -8x = -4 + 8x + 12x2

Solving for variable 'x'.

Reorder the terms:
12 + 4 + -8x + -8x + -12x2 = -4 + 8x + 12x2 + 4 + -8x + -12x2

Combine like terms: 12 + 4 = 16
16 + -8x + -8x + -12x2 = -4 + 8x + 12x2 + 4 + -8x + -12x2

Combine like terms: -8x + -8x = -16x
16 + -16x + -12x2 = -4 + 8x + 12x2 + 4 + -8x + -12x2

Reorder the terms:
16 + -16x + -12x2 = -4 + 4 + 8x + -8x + 12x2 + -12x2

Combine like terms: -4 + 4 = 0
16 + -16x + -12x2 = 0 + 8x + -8x + 12x2 + -12x2
16 + -16x + -12x2 = 8x + -8x + 12x2 + -12x2

Combine like terms: 8x + -8x = 0
16 + -16x + -12x2 = 0 + 12x2 + -12x2
16 + -16x + -12x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
16 + -16x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(4 + -4x + -3x2) = 0

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

Ignore the factor 4.

Subproblem 1
Set the factor '(2 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3x = 0 + -2

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

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

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667

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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

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

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

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

Simplifying
x = -2
Solution
x = {0.6666666667, -2}

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