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

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


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

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

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

Multiply (-5 + 3x) * (3 + 8x)
(-5(3 + 8x) + 3x * (3 + 8x)) = 0
((3 * -5 + 8x * -5) + 3x * (3 + 8x)) = 0
((-15 + -40x) + 3x * (3 + 8x)) = 0
(-15 + -40x + (3 * 3x + 8x * 3x)) = 0
(-15 + -40x + (9x + 24x2)) = 0

Combine like terms: -40x + 9x = -31x
(-15 + -31x + 24x2) = 0

Solving
-15 + -31x + 24x2 = 0

Solving for variable 'x'.

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

Subproblem 1

Set the factor '(-3 + -8x)' equal to zero and attempt to solve: Simplifying -3 + -8x = 0 Solving -3 + -8x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -8x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -8x = 0 + 3 -8x = 0 + 3 Combine like terms: 0 + 3 = 3 -8x = 3 Divide each side by '-8'. x = -0.375 Simplifying x = -0.375

Subproblem 2

Set the factor '(5 + -3x)' equal to zero and attempt to solve: Simplifying 5 + -3x = 0 Solving 5 + -3x = 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 + -3x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3x = 0 + -5 -3x = 0 + -5 Combine like terms: 0 + -5 = -5 -3x = -5 Divide each side by '-3'. x = 1.666666667 Simplifying x = 1.666666667

Solution

x = {-0.375, 1.666666667}

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