(3x-2)(3x+5)=260

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Solution for (3x-2)(3x+5)=260 equation: 


Simplifying
(3x + -2)(3x + 5) = 260

Reorder the terms:
(-2 + 3x)(3x + 5) = 260

Reorder the terms:
(-2 + 3x)(5 + 3x) = 260

Multiply (-2 + 3x) * (5 + 3x)
(-2(5 + 3x) + 3x * (5 + 3x)) = 260
((5 * -2 + 3x * -2) + 3x * (5 + 3x)) = 260
((-10 + -6x) + 3x * (5 + 3x)) = 260
(-10 + -6x + (5 * 3x + 3x * 3x)) = 260
(-10 + -6x + (15x + 9x2)) = 260

Combine like terms: -6x + 15x = 9x
(-10 + 9x + 9x2) = 260

Solving
-10 + 9x + 9x2 = 260

Solving for variable 'x'.

Reorder the terms:
-10 + -260 + 9x + 9x2 = 260 + -260

Combine like terms: -10 + -260 = -270
-270 + 9x + 9x2 = 260 + -260

Combine like terms: 260 + -260 = 0
-270 + 9x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(-30 + x + x2) = 0

Factor a trinomial.
9((-6 + -1x)(5 + -1x)) = 0

Ignore the factor 9.

Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-6, 5}

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