(3x-8)(6x+5)=0

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Solution for (3x-8)(6x+5)=0 equation:


Simplifying
(3x + -8)(6x + 5) = 0

Reorder the terms:
(-8 + 3x)(6x + 5) = 0

Reorder the terms:
(-8 + 3x)(5 + 6x) = 0

Multiply (-8 + 3x) * (5 + 6x)
(-8(5 + 6x) + 3x * (5 + 6x)) = 0
((5 * -8 + 6x * -8) + 3x * (5 + 6x)) = 0
((-40 + -48x) + 3x * (5 + 6x)) = 0
(-40 + -48x + (5 * 3x + 6x * 3x)) = 0
(-40 + -48x + (15x + 18x2)) = 0

Combine like terms: -48x + 15x = -33x
(-40 + -33x + 18x2) = 0

Solving
-40 + -33x + 18x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-5 + -6x)(8 + -3x) = 0

Subproblem 1

Set the factor '(-5 + -6x)' equal to zero and attempt to solve: Simplifying -5 + -6x = 0 Solving -5 + -6x = 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 + -6x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -6x = 0 + 5 -6x = 0 + 5 Combine like terms: 0 + 5 = 5 -6x = 5 Divide each side by '-6'. x = -0.8333333333 Simplifying x = -0.8333333333

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 = {-0.8333333333, 2.666666667}

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