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

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


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

Reorder the terms:
3x(-9 + 4x) = 5(2x + -5)
(-9 * 3x + 4x * 3x) = 5(2x + -5)
(-27x + 12x2) = 5(2x + -5)

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

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

Solving for variable 'x'.

Reorder the terms:
25 + -27x + -10x + 12x2 = -25 + 10x + 25 + -10x

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

Reorder the terms:
25 + -37x + 12x2 = -25 + 25 + 10x + -10x

Combine like terms: -25 + 25 = 0
25 + -37x + 12x2 = 0 + 10x + -10x
25 + -37x + 12x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
25 + -37x + 12x2 = 0

Factor a trinomial.
(1 + -1x)(25 + -12x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(25 + -12x)' equal to zero and attempt to solve:

Simplifying
25 + -12x = 0

Solving
25 + -12x = 0

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

Add '-25' to each side of the equation.
25 + -25 + -12x = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -12x = 0 + -25
-12x = 0 + -25

Combine like terms: 0 + -25 = -25
-12x = -25

Divide each side by '-12'.
x = 2.083333333

Simplifying
x = 2.083333333
Solution
x = {1, 2.083333333}

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