2x+14=(2x+14)(x-5)

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Solution for 2x+14=(2x+14)(x-5) equation: 


Simplifying
2x + 14 = (2x + 14)(x + -5)

Reorder the terms:
14 + 2x = (2x + 14)(x + -5)

Reorder the terms:
14 + 2x = (14 + 2x)(x + -5)

Reorder the terms:
14 + 2x = (14 + 2x)(-5 + x)

Multiply (14 + 2x) * (-5 + x)
14 + 2x = (14(-5 + x) + 2x * (-5 + x))
14 + 2x = ((-5 * 14 + x * 14) + 2x * (-5 + x))
14 + 2x = ((-70 + 14x) + 2x * (-5 + x))
14 + 2x = (-70 + 14x + (-5 * 2x + x * 2x))
14 + 2x = (-70 + 14x + (-10x + 2x2))

Combine like terms: 14x + -10x = 4x
14 + 2x = (-70 + 4x + 2x2)

Solving
14 + 2x = -70 + 4x + 2x2

Solving for variable 'x'.

Reorder the terms:
14 + 70 + 2x + -4x + -2x2 = -70 + 4x + 2x2 + 70 + -4x + -2x2

Combine like terms: 14 + 70 = 84
84 + 2x + -4x + -2x2 = -70 + 4x + 2x2 + 70 + -4x + -2x2

Combine like terms: 2x + -4x = -2x
84 + -2x + -2x2 = -70 + 4x + 2x2 + 70 + -4x + -2x2

Reorder the terms:
84 + -2x + -2x2 = -70 + 70 + 4x + -4x + 2x2 + -2x2

Combine like terms: -70 + 70 = 0
84 + -2x + -2x2 = 0 + 4x + -4x + 2x2 + -2x2
84 + -2x + -2x2 = 4x + -4x + 2x2 + -2x2

Combine like terms: 4x + -4x = 0
84 + -2x + -2x2 = 0 + 2x2 + -2x2
84 + -2x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
84 + -2x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(42 + -1x + -1x2) = 0

Factor a trinomial.
2((6 + -1x)(7 + x)) = 0

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

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

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7
Solution
x = {6, -7}

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