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

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


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

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

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

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

Combine like terms: 15x + -6x = 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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