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

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


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

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

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

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

Combine like terms: -40x + 6x = -34x
(-16 + -34x + 15x2) = 0

Solving
-16 + -34x + 15x2 = 0

Solving for variable 'x'.

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

Subproblem 1

Set the factor '(-2 + -5x)' equal to zero and attempt to solve: Simplifying -2 + -5x = 0 Solving -2 + -5x = 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 + -5x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -5x = 0 + 2 -5x = 0 + 2 Combine like terms: 0 + 2 = 2 -5x = 2 Divide each side by '-5'. x = -0.4 Simplifying x = -0.4

Subproblem 2

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

Solution

x = {-0.4, 2.666666667}

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