2(x+3)(x-5)=2(x-1)+8

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Solution for 2(x+3)(x-5)=2(x-1)+8 equation: 


Simplifying
2(x + 3)(x + -5) = 2(x + -1) + 8

Reorder the terms:
2(3 + x)(x + -5) = 2(x + -1) + 8

Reorder the terms:
2(3 + x)(-5 + x) = 2(x + -1) + 8

Multiply (3 + x) * (-5 + x)
2(3(-5 + x) + x(-5 + x)) = 2(x + -1) + 8
2((-5 * 3 + x * 3) + x(-5 + x)) = 2(x + -1) + 8
2((-15 + 3x) + x(-5 + x)) = 2(x + -1) + 8
2(-15 + 3x + (-5 * x + x * x)) = 2(x + -1) + 8
2(-15 + 3x + (-5x + x2)) = 2(x + -1) + 8

Combine like terms: 3x + -5x = -2x
2(-15 + -2x + x2) = 2(x + -1) + 8
(-15 * 2 + -2x * 2 + x2 * 2) = 2(x + -1) + 8
(-30 + -4x + 2x2) = 2(x + -1) + 8

Reorder the terms:
-30 + -4x + 2x2 = 2(-1 + x) + 8
-30 + -4x + 2x2 = (-1 * 2 + x * 2) + 8
-30 + -4x + 2x2 = (-2 + 2x) + 8

Reorder the terms:
-30 + -4x + 2x2 = -2 + 8 + 2x

Combine like terms: -2 + 8 = 6
-30 + -4x + 2x2 = 6 + 2x

Solving
-30 + -4x + 2x2 = 6 + 2x

Solving for variable 'x'.

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

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), '2'.
2(-18 + -3x + x2) = 0

Factor a trinomial.
2((-3 + -1x)(6 + -1x)) = 0

Ignore the factor 2.

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

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

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

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

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 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 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-3, 6}

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