3x(4x+34)=5x(2+9x)

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Solution for 3x(4x+34)=5x(2+9x) equation: 


Simplifying
3x(4x + 34) = 5x(2 + 9x)

Reorder the terms:
3x(34 + 4x) = 5x(2 + 9x)
(34 * 3x + 4x * 3x) = 5x(2 + 9x)
(102x + 12x2) = 5x(2 + 9x)
102x + 12x2 = (2 * 5x + 9x * 5x)
102x + 12x2 = (10x + 45x2)

Solving
102x + 12x2 = 10x + 45x2

Solving for variable 'x'.

Reorder the terms:
102x + -10x + 12x2 + -45x2 = 10x + 45x2 + -10x + -45x2

Combine like terms: 102x + -10x = 92x
92x + 12x2 + -45x2 = 10x + 45x2 + -10x + -45x2

Combine like terms: 12x2 + -45x2 = -33x2
92x + -33x2 = 10x + 45x2 + -10x + -45x2

Reorder the terms:
92x + -33x2 = 10x + -10x + 45x2 + -45x2

Combine like terms: 10x + -10x = 0
92x + -33x2 = 0 + 45x2 + -45x2
92x + -33x2 = 45x2 + -45x2

Combine like terms: 45x2 + -45x2 = 0
92x + -33x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(92 + -33x) = 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 '(92 + -33x)' equal to zero and attempt to solve:

Simplifying
92 + -33x = 0

Solving
92 + -33x = 0

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

Add '-92' to each side of the equation.
92 + -92 + -33x = 0 + -92

Combine like terms: 92 + -92 = 0
0 + -33x = 0 + -92
-33x = 0 + -92

Combine like terms: 0 + -92 = -92
-33x = -92

Divide each side by '-33'.
x = 2.787878788

Simplifying
x = 2.787878788
Solution
x = {0, 2.787878788}

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