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

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


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

Reorder the terms:
3(-2 + x)(2x + -5) = 4(x + -2)

Reorder the terms:
3(-2 + x)(-5 + 2x) = 4(x + -2)

Multiply (-2 + x) * (-5 + 2x)
3(-2(-5 + 2x) + x(-5 + 2x)) = 4(x + -2)
3((-5 * -2 + 2x * -2) + x(-5 + 2x)) = 4(x + -2)
3((10 + -4x) + x(-5 + 2x)) = 4(x + -2)
3(10 + -4x + (-5 * x + 2x * x)) = 4(x + -2)
3(10 + -4x + (-5x + 2x2)) = 4(x + -2)

Combine like terms: -4x + -5x = -9x
3(10 + -9x + 2x2) = 4(x + -2)
(10 * 3 + -9x * 3 + 2x2 * 3) = 4(x + -2)
(30 + -27x + 6x2) = 4(x + -2)

Reorder the terms:
30 + -27x + 6x2 = 4(-2 + x)
30 + -27x + 6x2 = (-2 * 4 + x * 4)
30 + -27x + 6x2 = (-8 + 4x)

Solving
30 + -27x + 6x2 = -8 + 4x

Solving for variable 'x'.

Reorder the terms:
30 + 8 + -27x + -4x + 6x2 = -8 + 4x + 8 + -4x

Combine like terms: 30 + 8 = 38
38 + -27x + -4x + 6x2 = -8 + 4x + 8 + -4x

Combine like terms: -27x + -4x = -31x
38 + -31x + 6x2 = -8 + 4x + 8 + -4x

Reorder the terms:
38 + -31x + 6x2 = -8 + 8 + 4x + -4x

Combine like terms: -8 + 8 = 0
38 + -31x + 6x2 = 0 + 4x + -4x
38 + -31x + 6x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
38 + -31x + 6x2 = 0

Factor a trinomial.
(2 + -1x)(19 + -6x) = 0


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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 2
Set the factor '(19 + -6x)' equal to zero and attempt to solve:

Simplifying
19 + -6x = 0

Solving
19 + -6x = 0

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

Add '-19' to each side of the equation.
19 + -19 + -6x = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -6x = 0 + -19
-6x = 0 + -19

Combine like terms: 0 + -19 = -19
-6x = -19

Divide each side by '-6'.
x = 3.166666667

Simplifying
x = 3.166666667
Solution
x = {2, 3.166666667}

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