(3x+8)(2x-5)=0

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Solution for (3x+8)(2x-5)=0 equation:


Simplifying
(3x + 8)(2x + -5) = 0

Reorder the terms:
(8 + 3x)(2x + -5) = 0

Reorder the terms:
(8 + 3x)(-5 + 2x) = 0

Multiply (8 + 3x) * (-5 + 2x)
(8(-5 + 2x) + 3x * (-5 + 2x)) = 0
((-5 * 8 + 2x * 8) + 3x * (-5 + 2x)) = 0
((-40 + 16x) + 3x * (-5 + 2x)) = 0
(-40 + 16x + (-5 * 3x + 2x * 3x)) = 0
(-40 + 16x + (-15x + 6x2)) = 0

Combine like terms: 16x + -15x = 1x
(-40 + 1x + 6x2) = 0

Solving
-40 + 1x + 6x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-8 + -3x)(5 + -2x) = 0

Subproblem 1

Set the factor '(-8 + -3x)' equal to zero and attempt to solve: Simplifying -8 + -3x = 0 Solving -8 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -3x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -3x = 0 + 8 -3x = 0 + 8 Combine like terms: 0 + 8 = 8 -3x = 8 Divide each side by '-3'. x = -2.666666667 Simplifying x = -2.666666667

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 = {-2.666666667, 2.5}

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