(2x-5)(3x+6)=0

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Solution for (2x-5)(3x+6)=0 equation:


Simplifying
(2x + -5)(3x + 6) = 0

Reorder the terms:
(-5 + 2x)(3x + 6) = 0

Reorder the terms:
(-5 + 2x)(6 + 3x) = 0

Multiply (-5 + 2x) * (6 + 3x)
(-5(6 + 3x) + 2x * (6 + 3x)) = 0
((6 * -5 + 3x * -5) + 2x * (6 + 3x)) = 0
((-30 + -15x) + 2x * (6 + 3x)) = 0
(-30 + -15x + (6 * 2x + 3x * 2x)) = 0
(-30 + -15x + (12x + 6x2)) = 0

Combine like terms: -15x + 12x = -3x
(-30 + -3x + 6x2) = 0

Solving
-30 + -3x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-10 + -1x + 2x2) = 0

Factor a trinomial.
3((-2 + -1x)(5 + -2x)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 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 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2

Subproblem 2

Set the factor '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 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 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5

Solution

x = {-2, 2.5}

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