170=(3x+5)(3x-2)

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Solution for 170=(3x+5)(3x-2) equation: 


Simplifying
170 = (3x + 5)(3x + -2)

Reorder the terms:
170 = (5 + 3x)(3x + -2)

Reorder the terms:
170 = (5 + 3x)(-2 + 3x)

Multiply (5 + 3x) * (-2 + 3x)
170 = (5(-2 + 3x) + 3x * (-2 + 3x))
170 = ((-2 * 5 + 3x * 5) + 3x * (-2 + 3x))
170 = ((-10 + 15x) + 3x * (-2 + 3x))
170 = (-10 + 15x + (-2 * 3x + 3x * 3x))
170 = (-10 + 15x + (-6x + 9x2))

Combine like terms: 15x + -6x = 9x
170 = (-10 + 9x + 9x2)

Solving
170 = -10 + 9x + 9x2

Solving for variable 'x'.

Combine like terms: 170 + 10 = 180
180 + -9x + -9x2 = -10 + 9x + 9x2 + 10 + -9x + -9x2

Reorder the terms:
180 + -9x + -9x2 = -10 + 10 + 9x + -9x + 9x2 + -9x2

Combine like terms: -10 + 10 = 0
180 + -9x + -9x2 = 0 + 9x + -9x + 9x2 + -9x2
180 + -9x + -9x2 = 9x + -9x + 9x2 + -9x2

Combine like terms: 9x + -9x = 0
180 + -9x + -9x2 = 0 + 9x2 + -9x2
180 + -9x + -9x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
180 + -9x + -9x2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(20 + -1x + -1x2) = 0

Factor a trinomial.
9((4 + -1x)(5 + x)) = 0

Ignore the factor 9.

Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

Subproblem 2
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
Solution
x = {4, -5}

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