(x-18)*(3x-10)-(3x-10)*(3x-10)=0

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Solution for (x-18)*(3x-10)-(3x-10)*(3x-10)=0 equation: 


Simplifying
(x + -18)(3x + -10) + -1(3x + -10)(3x + -10) = 0

Reorder the terms:
(-18 + x)(3x + -10) + -1(3x + -10)(3x + -10) = 0

Reorder the terms:
(-18 + x)(-10 + 3x) + -1(3x + -10)(3x + -10) = 0

Multiply (-18 + x) * (-10 + 3x)
(-18(-10 + 3x) + x(-10 + 3x)) + -1(3x + -10)(3x + -10) = 0
((-10 * -18 + 3x * -18) + x(-10 + 3x)) + -1(3x + -10)(3x + -10) = 0
((180 + -54x) + x(-10 + 3x)) + -1(3x + -10)(3x + -10) = 0
(180 + -54x + (-10 * x + 3x * x)) + -1(3x + -10)(3x + -10) = 0
(180 + -54x + (-10x + 3x2)) + -1(3x + -10)(3x + -10) = 0

Combine like terms: -54x + -10x = -64x
(180 + -64x + 3x2) + -1(3x + -10)(3x + -10) = 0

Reorder the terms:
180 + -64x + 3x2 + -1(-10 + 3x)(3x + -10) = 0

Reorder the terms:
180 + -64x + 3x2 + -1(-10 + 3x)(-10 + 3x) = 0

Multiply (-10 + 3x) * (-10 + 3x)
180 + -64x + 3x2 + -1(-10(-10 + 3x) + 3x * (-10 + 3x)) = 0
180 + -64x + 3x2 + -1((-10 * -10 + 3x * -10) + 3x * (-10 + 3x)) = 0
180 + -64x + 3x2 + -1((100 + -30x) + 3x * (-10 + 3x)) = 0
180 + -64x + 3x2 + -1(100 + -30x + (-10 * 3x + 3x * 3x)) = 0
180 + -64x + 3x2 + -1(100 + -30x + (-30x + 9x2)) = 0

Combine like terms: -30x + -30x = -60x
180 + -64x + 3x2 + -1(100 + -60x + 9x2) = 0
180 + -64x + 3x2 + (100 * -1 + -60x * -1 + 9x2 * -1) = 0
180 + -64x + 3x2 + (-100 + 60x + -9x2) = 0

Reorder the terms:
180 + -100 + -64x + 60x + 3x2 + -9x2 = 0

Combine like terms: 180 + -100 = 80
80 + -64x + 60x + 3x2 + -9x2 = 0

Combine like terms: -64x + 60x = -4x
80 + -4x + 3x2 + -9x2 = 0

Combine like terms: 3x2 + -9x2 = -6x2
80 + -4x + -6x2 = 0

Solving
80 + -4x + -6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(40 + -2x + -3x2) = 0

Factor a trinomial.
2((10 + -3x)(4 + x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(10 + -3x)' equal to zero and attempt to solve:

Simplifying
10 + -3x = 0

Solving
10 + -3x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -3x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -3x = 0 + -10
-3x = 0 + -10

Combine like terms: 0 + -10 = -10
-3x = -10

Divide each side by '-3'.
x = 3.333333333

Simplifying
x = 3.333333333

Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {3.333333333, -4}

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