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

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


Simplifying
0 = 2(x + -5)(3x + -2)

Reorder the terms:
0 = 2(-5 + x)(3x + -2)

Reorder the terms:
0 = 2(-5 + x)(-2 + 3x)

Multiply (-5 + x) * (-2 + 3x)
0 = 2(-5(-2 + 3x) + x(-2 + 3x))
0 = 2((-2 * -5 + 3x * -5) + x(-2 + 3x))
0 = 2((10 + -15x) + x(-2 + 3x))
0 = 2(10 + -15x + (-2 * x + 3x * x))
0 = 2(10 + -15x + (-2x + 3x2))

Combine like terms: -15x + -2x = -17x
0 = 2(10 + -17x + 3x2)
0 = (10 * 2 + -17x * 2 + 3x2 * 2)
0 = (20 + -34x + 6x2)

Solving
0 = 20 + -34x + 6x2

Solving for variable 'x'.

Combine like terms: 0 + -20 = -20
-20 + 34x + -6x2 = 20 + -34x + 6x2 + -20 + 34x + -6x2

Reorder the terms:
-20 + 34x + -6x2 = 20 + -20 + -34x + 34x + 6x2 + -6x2

Combine like terms: 20 + -20 = 0
-20 + 34x + -6x2 = 0 + -34x + 34x + 6x2 + -6x2
-20 + 34x + -6x2 = -34x + 34x + 6x2 + -6x2

Combine like terms: -34x + 34x = 0
-20 + 34x + -6x2 = 0 + 6x2 + -6x2
-20 + 34x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-20 + 34x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + 17x + -3x2) = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve:

Simplifying
-5 + x = 0

Solving
-5 + x = 0

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

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

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

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

Simplifying
x = 5

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

Simplifying
2 + -3x = 0

Solving
2 + -3x = 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 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Solution
x = {5, 0.6666666667}

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