(1600+18x)(x-15)=(1200+22x)(x-15)

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Solution for (1600+18x)(x-15)=(1200+22x)(x-15) equation: 


Simplifying
(1600 + 18x)(x + -15) = (1200 + 22x)(x + -15)

Reorder the terms:
(1600 + 18x)(-15 + x) = (1200 + 22x)(x + -15)

Multiply (1600 + 18x) * (-15 + x)
(1600(-15 + x) + 18x * (-15 + x)) = (1200 + 22x)(x + -15)
((-15 * 1600 + x * 1600) + 18x * (-15 + x)) = (1200 + 22x)(x + -15)
((-24000 + 1600x) + 18x * (-15 + x)) = (1200 + 22x)(x + -15)
(-24000 + 1600x + (-15 * 18x + x * 18x)) = (1200 + 22x)(x + -15)
(-24000 + 1600x + (-270x + 18x2)) = (1200 + 22x)(x + -15)

Combine like terms: 1600x + -270x = 1330x
(-24000 + 1330x + 18x2) = (1200 + 22x)(x + -15)

Reorder the terms:
-24000 + 1330x + 18x2 = (1200 + 22x)(-15 + x)

Multiply (1200 + 22x) * (-15 + x)
-24000 + 1330x + 18x2 = (1200(-15 + x) + 22x * (-15 + x))
-24000 + 1330x + 18x2 = ((-15 * 1200 + x * 1200) + 22x * (-15 + x))
-24000 + 1330x + 18x2 = ((-18000 + 1200x) + 22x * (-15 + x))
-24000 + 1330x + 18x2 = (-18000 + 1200x + (-15 * 22x + x * 22x))
-24000 + 1330x + 18x2 = (-18000 + 1200x + (-330x + 22x2))

Combine like terms: 1200x + -330x = 870x
-24000 + 1330x + 18x2 = (-18000 + 870x + 22x2)

Solving
-24000 + 1330x + 18x2 = -18000 + 870x + 22x2

Solving for variable 'x'.

Reorder the terms:
-24000 + 18000 + 1330x + -870x + 18x2 + -22x2 = -18000 + 870x + 22x2 + 18000 + -870x + -22x2

Combine like terms: -24000 + 18000 = -6000
-6000 + 1330x + -870x + 18x2 + -22x2 = -18000 + 870x + 22x2 + 18000 + -870x + -22x2

Combine like terms: 1330x + -870x = 460x
-6000 + 460x + 18x2 + -22x2 = -18000 + 870x + 22x2 + 18000 + -870x + -22x2

Combine like terms: 18x2 + -22x2 = -4x2
-6000 + 460x + -4x2 = -18000 + 870x + 22x2 + 18000 + -870x + -22x2

Reorder the terms:
-6000 + 460x + -4x2 = -18000 + 18000 + 870x + -870x + 22x2 + -22x2

Combine like terms: -18000 + 18000 = 0
-6000 + 460x + -4x2 = 0 + 870x + -870x + 22x2 + -22x2
-6000 + 460x + -4x2 = 870x + -870x + 22x2 + -22x2

Combine like terms: 870x + -870x = 0
-6000 + 460x + -4x2 = 0 + 22x2 + -22x2
-6000 + 460x + -4x2 = 22x2 + -22x2

Combine like terms: 22x2 + -22x2 = 0
-6000 + 460x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-1500 + 115x + -1x2) = 0

Factor a trinomial.
4((-100 + x)(15 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-100 + x)' equal to zero and attempt to solve:

Simplifying
-100 + x = 0

Solving
-100 + x = 0

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

Add '100' to each side of the equation.
-100 + 100 + x = 0 + 100

Combine like terms: -100 + 100 = 0
0 + x = 0 + 100
x = 0 + 100

Combine like terms: 0 + 100 = 100
x = 100

Simplifying
x = 100

Subproblem 2
Set the factor '(15 + -1x)' equal to zero and attempt to solve:

Simplifying
15 + -1x = 0

Solving
15 + -1x = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1x = 0 + -15
-1x = 0 + -15

Combine like terms: 0 + -15 = -15
-1x = -15

Divide each side by '-1'.
x = 15

Simplifying
x = 15
Solution
x = {100, 15}

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