(2x-3)(x+6)=(x-9)(x+2)

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Solution for (2x-3)(x+6)=(x-9)(x+2) equation: 


Simplifying
(2x + -3)(x + 6) = (x + -9)(x + 2)

Reorder the terms:
(-3 + 2x)(x + 6) = (x + -9)(x + 2)

Reorder the terms:
(-3 + 2x)(6 + x) = (x + -9)(x + 2)

Multiply (-3 + 2x) * (6 + x)
(-3(6 + x) + 2x * (6 + x)) = (x + -9)(x + 2)
((6 * -3 + x * -3) + 2x * (6 + x)) = (x + -9)(x + 2)
((-18 + -3x) + 2x * (6 + x)) = (x + -9)(x + 2)
(-18 + -3x + (6 * 2x + x * 2x)) = (x + -9)(x + 2)
(-18 + -3x + (12x + 2x2)) = (x + -9)(x + 2)

Combine like terms: -3x + 12x = 9x
(-18 + 9x + 2x2) = (x + -9)(x + 2)

Reorder the terms:
-18 + 9x + 2x2 = (-9 + x)(x + 2)

Reorder the terms:
-18 + 9x + 2x2 = (-9 + x)(2 + x)

Multiply (-9 + x) * (2 + x)
-18 + 9x + 2x2 = (-9(2 + x) + x(2 + x))
-18 + 9x + 2x2 = ((2 * -9 + x * -9) + x(2 + x))
-18 + 9x + 2x2 = ((-18 + -9x) + x(2 + x))
-18 + 9x + 2x2 = (-18 + -9x + (2 * x + x * x))
-18 + 9x + 2x2 = (-18 + -9x + (2x + x2))

Combine like terms: -9x + 2x = -7x
-18 + 9x + 2x2 = (-18 + -7x + x2)

Add '18' to each side of the equation.
-18 + 9x + 18 + 2x2 = -18 + -7x + 18 + x2

Reorder the terms:
-18 + 18 + 9x + 2x2 = -18 + -7x + 18 + x2

Combine like terms: -18 + 18 = 0
0 + 9x + 2x2 = -18 + -7x + 18 + x2
9x + 2x2 = -18 + -7x + 18 + x2

Reorder the terms:
9x + 2x2 = -18 + 18 + -7x + x2

Combine like terms: -18 + 18 = 0
9x + 2x2 = 0 + -7x + x2
9x + 2x2 = -7x + x2

Solving
9x + 2x2 = -7x + x2

Solving for variable 'x'.

Reorder the terms:
9x + 7x + 2x2 + -1x2 = -7x + x2 + 7x + -1x2

Combine like terms: 9x + 7x = 16x
16x + 2x2 + -1x2 = -7x + x2 + 7x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
16x + 1x2 = -7x + x2 + 7x + -1x2

Reorder the terms:
16x + 1x2 = -7x + 7x + x2 + -1x2

Combine like terms: -7x + 7x = 0
16x + 1x2 = 0 + x2 + -1x2
16x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
16x + 1x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(16 + x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(16 + x)' equal to zero and attempt to solve:

Simplifying
16 + x = 0

Solving
16 + x = 0

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

Add '-16' to each side of the equation.
16 + -16 + x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + x = 0 + -16
x = 0 + -16

Combine like terms: 0 + -16 = -16
x = -16

Simplifying
x = -16
Solution
x = {0, -16}

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