(6x+16)*(2x)=(2x+18)*(4x)

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Solution for (6x+16)*(2x)=(2x+18)*(4x) equation: 


Simplifying
(6x + 16)(2x) = (2x + 18)(4x)

Reorder the terms:
(16 + 6x)(2x) = (2x + 18)(4x)

Remove parenthesis around (2x)
(16 + 6x) * 2x = (2x + 18)(4x)

Reorder the terms for easier multiplication:
2x(16 + 6x) = (2x + 18)(4x)
(16 * 2x + 6x * 2x) = (2x + 18)(4x)
(32x + 12x2) = (2x + 18)(4x)

Reorder the terms:
32x + 12x2 = (18 + 2x)(4x)

Remove parenthesis around (4x)
32x + 12x2 = (18 + 2x) * 4x

Reorder the terms for easier multiplication:
32x + 12x2 = 4x(18 + 2x)
32x + 12x2 = (18 * 4x + 2x * 4x)
32x + 12x2 = (72x + 8x2)

Solving
32x + 12x2 = 72x + 8x2

Solving for variable 'x'.

Reorder the terms:
32x + -72x + 12x2 + -8x2 = 72x + 8x2 + -72x + -8x2

Combine like terms: 32x + -72x = -40x
-40x + 12x2 + -8x2 = 72x + 8x2 + -72x + -8x2

Combine like terms: 12x2 + -8x2 = 4x2
-40x + 4x2 = 72x + 8x2 + -72x + -8x2

Reorder the terms:
-40x + 4x2 = 72x + -72x + 8x2 + -8x2

Combine like terms: 72x + -72x = 0
-40x + 4x2 = 0 + 8x2 + -8x2
-40x + 4x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
-40x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-10 + x) = 0

Ignore the factor 4.

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 '(-10 + x)' equal to zero and attempt to solve:

Simplifying
-10 + x = 0

Solving
-10 + x = 0

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

Add '10' to each side of the equation.
-10 + 10 + x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + x = 0 + 10
x = 0 + 10

Combine like terms: 0 + 10 = 10
x = 10

Simplifying
x = 10
Solution
x = {0, 10}

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