3*(4x-6)=2x*(5x-12)

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Solution for 3*(4x-6)=2x*(5x-12) equation: 


Simplifying
3(4x + -6) = 2x(5x + -12)

Reorder the terms:
3(-6 + 4x) = 2x(5x + -12)
(-6 * 3 + 4x * 3) = 2x(5x + -12)
(-18 + 12x) = 2x(5x + -12)

Reorder the terms:
-18 + 12x = 2x(-12 + 5x)
-18 + 12x = (-12 * 2x + 5x * 2x)
-18 + 12x = (-24x + 10x2)

Solving
-18 + 12x = -24x + 10x2

Solving for variable 'x'.

Combine like terms: 12x + 24x = 36x
-18 + 36x + -10x2 = -24x + 10x2 + 24x + -10x2

Reorder the terms:
-18 + 36x + -10x2 = -24x + 24x + 10x2 + -10x2

Combine like terms: -24x + 24x = 0
-18 + 36x + -10x2 = 0 + 10x2 + -10x2
-18 + 36x + -10x2 = 10x2 + -10x2

Combine like terms: 10x2 + -10x2 = 0
-18 + 36x + -10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + 18x + -5x2) = 0

Factor a trinomial.
2((-3 + x)(3 + -5x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-3 + x)' equal to zero and attempt to solve:

Simplifying
-3 + x = 0

Solving
-3 + x = 0

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

Add '3' to each side of the equation.
-3 + 3 + x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + x = 0 + 3
x = 0 + 3

Combine like terms: 0 + 3 = 3
x = 3

Simplifying
x = 3

Subproblem 2
Set the factor '(3 + -5x)' equal to zero and attempt to solve:

Simplifying
3 + -5x = 0

Solving
3 + -5x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -5x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5x = 0 + -3
-5x = 0 + -3

Combine like terms: 0 + -3 = -3
-5x = -3

Divide each side by '-5'.
x = 0.6

Simplifying
x = 0.6
Solution
x = {3, 0.6}

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