3(4x-9)=5x(2x-5)

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


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

Reorder the terms:
3(-9 + 4x) = 5x(2x + -5)
(-9 * 3 + 4x * 3) = 5x(2x + -5)
(-27 + 12x) = 5x(2x + -5)

Reorder the terms:
-27 + 12x = 5x(-5 + 2x)
-27 + 12x = (-5 * 5x + 2x * 5x)
-27 + 12x = (-25x + 10x2)

Solving
-27 + 12x = -25x + 10x2

Solving for variable 'x'.

Combine like terms: 12x + 25x = 37x
-27 + 37x + -10x2 = -25x + 10x2 + 25x + -10x2

Reorder the terms:
-27 + 37x + -10x2 = -25x + 25x + 10x2 + -10x2

Combine like terms: -25x + 25x = 0
-27 + 37x + -10x2 = 0 + 10x2 + -10x2
-27 + 37x + -10x2 = 10x2 + -10x2

Combine like terms: 10x2 + -10x2 = 0
-27 + 37x + -10x2 = 0

Factor a trinomial.
(-27 + 10x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-27 + 10x)' equal to zero and attempt to solve:

Simplifying
-27 + 10x = 0

Solving
-27 + 10x = 0

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

Add '27' to each side of the equation.
-27 + 27 + 10x = 0 + 27

Combine like terms: -27 + 27 = 0
0 + 10x = 0 + 27
10x = 0 + 27

Combine like terms: 0 + 27 = 27
10x = 27

Divide each side by '10'.
x = 2.7

Simplifying
x = 2.7

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {2.7, 1}

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