(5x+2)(x-4)=(2x+1)(x-14)

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Solution for (5x+2)(x-4)=(2x+1)(x-14) equation: 


Simplifying
(5x + 2)(x + -4) = (2x + 1)(x + -14)

Reorder the terms:
(2 + 5x)(x + -4) = (2x + 1)(x + -14)

Reorder the terms:
(2 + 5x)(-4 + x) = (2x + 1)(x + -14)

Multiply (2 + 5x) * (-4 + x)
(2(-4 + x) + 5x * (-4 + x)) = (2x + 1)(x + -14)
((-4 * 2 + x * 2) + 5x * (-4 + x)) = (2x + 1)(x + -14)
((-8 + 2x) + 5x * (-4 + x)) = (2x + 1)(x + -14)
(-8 + 2x + (-4 * 5x + x * 5x)) = (2x + 1)(x + -14)
(-8 + 2x + (-20x + 5x2)) = (2x + 1)(x + -14)

Combine like terms: 2x + -20x = -18x
(-8 + -18x + 5x2) = (2x + 1)(x + -14)

Reorder the terms:
-8 + -18x + 5x2 = (1 + 2x)(x + -14)

Reorder the terms:
-8 + -18x + 5x2 = (1 + 2x)(-14 + x)

Multiply (1 + 2x) * (-14 + x)
-8 + -18x + 5x2 = (1(-14 + x) + 2x * (-14 + x))
-8 + -18x + 5x2 = ((-14 * 1 + x * 1) + 2x * (-14 + x))
-8 + -18x + 5x2 = ((-14 + 1x) + 2x * (-14 + x))
-8 + -18x + 5x2 = (-14 + 1x + (-14 * 2x + x * 2x))
-8 + -18x + 5x2 = (-14 + 1x + (-28x + 2x2))

Combine like terms: 1x + -28x = -27x
-8 + -18x + 5x2 = (-14 + -27x + 2x2)

Solving
-8 + -18x + 5x2 = -14 + -27x + 2x2

Solving for variable 'x'.

Reorder the terms:
-8 + 14 + -18x + 27x + 5x2 + -2x2 = -14 + -27x + 2x2 + 14 + 27x + -2x2

Combine like terms: -8 + 14 = 6
6 + -18x + 27x + 5x2 + -2x2 = -14 + -27x + 2x2 + 14 + 27x + -2x2

Combine like terms: -18x + 27x = 9x
6 + 9x + 5x2 + -2x2 = -14 + -27x + 2x2 + 14 + 27x + -2x2

Combine like terms: 5x2 + -2x2 = 3x2
6 + 9x + 3x2 = -14 + -27x + 2x2 + 14 + 27x + -2x2

Reorder the terms:
6 + 9x + 3x2 = -14 + 14 + -27x + 27x + 2x2 + -2x2

Combine like terms: -14 + 14 = 0
6 + 9x + 3x2 = 0 + -27x + 27x + 2x2 + -2x2
6 + 9x + 3x2 = -27x + 27x + 2x2 + -2x2

Combine like terms: -27x + 27x = 0
6 + 9x + 3x2 = 0 + 2x2 + -2x2
6 + 9x + 3x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
6 + 9x + 3x2 = 0

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

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

Ignore the factor 3.

Subproblem 1
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

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

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {-2, -1}

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