(2x+1)(x-16)=(3x-2)(x-6)

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Solution for (2x+1)(x-16)=(3x-2)(x-6) equation: 


Simplifying
(2x + 1)(x + -16) = (3x + -2)(x + -6)

Reorder the terms:
(1 + 2x)(x + -16) = (3x + -2)(x + -6)

Reorder the terms:
(1 + 2x)(-16 + x) = (3x + -2)(x + -6)

Multiply (1 + 2x) * (-16 + x)
(1(-16 + x) + 2x * (-16 + x)) = (3x + -2)(x + -6)
((-16 * 1 + x * 1) + 2x * (-16 + x)) = (3x + -2)(x + -6)
((-16 + 1x) + 2x * (-16 + x)) = (3x + -2)(x + -6)
(-16 + 1x + (-16 * 2x + x * 2x)) = (3x + -2)(x + -6)
(-16 + 1x + (-32x + 2x2)) = (3x + -2)(x + -6)

Combine like terms: 1x + -32x = -31x
(-16 + -31x + 2x2) = (3x + -2)(x + -6)

Reorder the terms:
-16 + -31x + 2x2 = (-2 + 3x)(x + -6)

Reorder the terms:
-16 + -31x + 2x2 = (-2 + 3x)(-6 + x)

Multiply (-2 + 3x) * (-6 + x)
-16 + -31x + 2x2 = (-2(-6 + x) + 3x * (-6 + x))
-16 + -31x + 2x2 = ((-6 * -2 + x * -2) + 3x * (-6 + x))
-16 + -31x + 2x2 = ((12 + -2x) + 3x * (-6 + x))
-16 + -31x + 2x2 = (12 + -2x + (-6 * 3x + x * 3x))
-16 + -31x + 2x2 = (12 + -2x + (-18x + 3x2))

Combine like terms: -2x + -18x = -20x
-16 + -31x + 2x2 = (12 + -20x + 3x2)

Solving
-16 + -31x + 2x2 = 12 + -20x + 3x2

Solving for variable 'x'.

Reorder the terms:
-16 + -12 + -31x + 20x + 2x2 + -3x2 = 12 + -20x + 3x2 + -12 + 20x + -3x2

Combine like terms: -16 + -12 = -28
-28 + -31x + 20x + 2x2 + -3x2 = 12 + -20x + 3x2 + -12 + 20x + -3x2

Combine like terms: -31x + 20x = -11x
-28 + -11x + 2x2 + -3x2 = 12 + -20x + 3x2 + -12 + 20x + -3x2

Combine like terms: 2x2 + -3x2 = -1x2
-28 + -11x + -1x2 = 12 + -20x + 3x2 + -12 + 20x + -3x2

Reorder the terms:
-28 + -11x + -1x2 = 12 + -12 + -20x + 20x + 3x2 + -3x2

Combine like terms: 12 + -12 = 0
-28 + -11x + -1x2 = 0 + -20x + 20x + 3x2 + -3x2
-28 + -11x + -1x2 = -20x + 20x + 3x2 + -3x2

Combine like terms: -20x + 20x = 0
-28 + -11x + -1x2 = 0 + 3x2 + -3x2
-28 + -11x + -1x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-28 + -11x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(28 + 11x + x2) = 0

Factor a trinomial.
-1((7 + x)(4 + x)) = 0

Ignore the factor -1.

Subproblem 1
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

Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {-7, -4}

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