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

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


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

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

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

Multiply (5 + x) * (-2 + 3x)
(5(-2 + 3x) + x(-2 + 3x)) = 0
((-2 * 5 + 3x * 5) + x(-2 + 3x)) = 0
((-10 + 15x) + x(-2 + 3x)) = 0
(-10 + 15x + (-2 * x + 3x * x)) = 0
(-10 + 15x + (-2x + 3x2)) = 0

Combine like terms: 15x + -2x = 13x
(-10 + 13x + 3x2) = 0

Solving
-10 + 13x + 3x2 = 0

Solving for variable 'x'.

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

Subproblem 1

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

Subproblem 2

Set the factor '(2 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 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 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667

Solution

x = {-5, 0.6666666667}

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