2(x-5)-(2x-6)=(x+1)(3x-5)

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Solution for 2(x-5)-(2x-6)=(x+1)(3x-5) equation: 


Simplifying
2(x + -5) + -1(2x + -6) = (x + 1)(3x + -5)

Reorder the terms:
2(-5 + x) + -1(2x + -6) = (x + 1)(3x + -5)
(-5 * 2 + x * 2) + -1(2x + -6) = (x + 1)(3x + -5)
(-10 + 2x) + -1(2x + -6) = (x + 1)(3x + -5)

Reorder the terms:
-10 + 2x + -1(-6 + 2x) = (x + 1)(3x + -5)
-10 + 2x + (-6 * -1 + 2x * -1) = (x + 1)(3x + -5)
-10 + 2x + (6 + -2x) = (x + 1)(3x + -5)

Reorder the terms:
-10 + 6 + 2x + -2x = (x + 1)(3x + -5)

Combine like terms: -10 + 6 = -4
-4 + 2x + -2x = (x + 1)(3x + -5)

Combine like terms: 2x + -2x = 0
-4 + 0 = (x + 1)(3x + -5)
-4 = (x + 1)(3x + -5)

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

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

Multiply (1 + x) * (-5 + 3x)
-4 = (1(-5 + 3x) + x(-5 + 3x))
-4 = ((-5 * 1 + 3x * 1) + x(-5 + 3x))
-4 = ((-5 + 3x) + x(-5 + 3x))
-4 = (-5 + 3x + (-5 * x + 3x * x))
-4 = (-5 + 3x + (-5x + 3x2))

Combine like terms: 3x + -5x = -2x
-4 = (-5 + -2x + 3x2)

Solving
-4 = -5 + -2x + 3x2

Solving for variable 'x'.

Combine like terms: -4 + 5 = 1
1 + 2x + -3x2 = -5 + -2x + 3x2 + 5 + 2x + -3x2

Reorder the terms:
1 + 2x + -3x2 = -5 + 5 + -2x + 2x + 3x2 + -3x2

Combine like terms: -5 + 5 = 0
1 + 2x + -3x2 = 0 + -2x + 2x + 3x2 + -3x2
1 + 2x + -3x2 = -2x + 2x + 3x2 + -3x2

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

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

Factor a trinomial.
(1 + -1x)(1 + 3x) = 0


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 '(1 + 3x)' equal to zero and attempt to solve:

Simplifying
1 + 3x = 0

Solving
1 + 3x = 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 + 3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3x = 0 + -1
3x = 0 + -1

Combine like terms: 0 + -1 = -1
3x = -1

Divide each side by '3'.
x = -0.3333333333

Simplifying
x = -0.3333333333
Solution
x = {1, -0.3333333333}

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