34-34x=(6x+2)(x-1)

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Solution for 34-34x=(6x+2)(x-1) equation: 


Simplifying
34 + -34x = (6x + 2)(x + -1)

Reorder the terms:
34 + -34x = (2 + 6x)(x + -1)

Reorder the terms:
34 + -34x = (2 + 6x)(-1 + x)

Multiply (2 + 6x) * (-1 + x)
34 + -34x = (2(-1 + x) + 6x * (-1 + x))
34 + -34x = ((-1 * 2 + x * 2) + 6x * (-1 + x))
34 + -34x = ((-2 + 2x) + 6x * (-1 + x))
34 + -34x = (-2 + 2x + (-1 * 6x + x * 6x))
34 + -34x = (-2 + 2x + (-6x + 6x2))

Combine like terms: 2x + -6x = -4x
34 + -34x = (-2 + -4x + 6x2)

Solving
34 + -34x = -2 + -4x + 6x2

Solving for variable 'x'.

Reorder the terms:
34 + 2 + -34x + 4x + -6x2 = -2 + -4x + 6x2 + 2 + 4x + -6x2

Combine like terms: 34 + 2 = 36
36 + -34x + 4x + -6x2 = -2 + -4x + 6x2 + 2 + 4x + -6x2

Combine like terms: -34x + 4x = -30x
36 + -30x + -6x2 = -2 + -4x + 6x2 + 2 + 4x + -6x2

Reorder the terms:
36 + -30x + -6x2 = -2 + 2 + -4x + 4x + 6x2 + -6x2

Combine like terms: -2 + 2 = 0
36 + -30x + -6x2 = 0 + -4x + 4x + 6x2 + -6x2
36 + -30x + -6x2 = -4x + 4x + 6x2 + -6x2

Combine like terms: -4x + 4x = 0
36 + -30x + -6x2 = 0 + 6x2 + -6x2
36 + -30x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
36 + -30x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(6 + -5x + -1x2) = 0

Factor a trinomial.
6((1 + -1x)(6 + x)) = 0

Ignore the factor 6.

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1

Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Solution
x = {1, -6}

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