(3x-2)*(2x+18)-(3x-2)*(9x-17)=0

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Solution for (3x-2)*(2x+18)-(3x-2)*(9x-17)=0 equation:


Simplifying
(3x + -2)(2x + 18) + -1(3x + -2)(9x + -17) = 0

Reorder the terms:
(-2 + 3x)(2x + 18) + -1(3x + -2)(9x + -17) = 0

Reorder the terms:
(-2 + 3x)(18 + 2x) + -1(3x + -2)(9x + -17) = 0

Multiply (-2 + 3x) * (18 + 2x)
(-2(18 + 2x) + 3x * (18 + 2x)) + -1(3x + -2)(9x + -17) = 0
((18 * -2 + 2x * -2) + 3x * (18 + 2x)) + -1(3x + -2)(9x + -17) = 0
((-36 + -4x) + 3x * (18 + 2x)) + -1(3x + -2)(9x + -17) = 0
(-36 + -4x + (18 * 3x + 2x * 3x)) + -1(3x + -2)(9x + -17) = 0
(-36 + -4x + (54x + 6x2)) + -1(3x + -2)(9x + -17) = 0

Combine like terms: -4x + 54x = 50x
(-36 + 50x + 6x2) + -1(3x + -2)(9x + -17) = 0

Reorder the terms:
-36 + 50x + 6x2 + -1(-2 + 3x)(9x + -17) = 0

Reorder the terms:
-36 + 50x + 6x2 + -1(-2 + 3x)(-17 + 9x) = 0

Multiply (-2 + 3x) * (-17 + 9x)
-36 + 50x + 6x2 + -1(-2(-17 + 9x) + 3x * (-17 + 9x)) = 0
-36 + 50x + 6x2 + -1((-17 * -2 + 9x * -2) + 3x * (-17 + 9x)) = 0
-36 + 50x + 6x2 + -1((34 + -18x) + 3x * (-17 + 9x)) = 0
-36 + 50x + 6x2 + -1(34 + -18x + (-17 * 3x + 9x * 3x)) = 0
-36 + 50x + 6x2 + -1(34 + -18x + (-51x + 27x2)) = 0

Combine like terms: -18x + -51x = -69x
-36 + 50x + 6x2 + -1(34 + -69x + 27x2) = 0
-36 + 50x + 6x2 + (34 * -1 + -69x * -1 + 27x2 * -1) = 0
-36 + 50x + 6x2 + (-34 + 69x + -27x2) = 0

Reorder the terms:
-36 + -34 + 50x + 69x + 6x2 + -27x2 = 0

Combine like terms: -36 + -34 = -70
-70 + 50x + 69x + 6x2 + -27x2 = 0

Combine like terms: 50x + 69x = 119x
-70 + 119x + 6x2 + -27x2 = 0

Combine like terms: 6x2 + -27x2 = -21x2
-70 + 119x + -21x2 = 0

Solving
-70 + 119x + -21x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-10 + 17x + -3x2) = 0

Factor a trinomial.
7((-5 + x)(2 + -3x)) = 0

Ignore the factor 7.

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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