(3x+5)(4x-1)=0

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Solution for (3x+5)(4x-1)=0 equation:


Simplifying
(3x + 5)(4x + -1) = 0

Reorder the terms:
(5 + 3x)(4x + -1) = 0

Reorder the terms:
(5 + 3x)(-1 + 4x) = 0

Multiply (5 + 3x) * (-1 + 4x)
(5(-1 + 4x) + 3x * (-1 + 4x)) = 0
((-1 * 5 + 4x * 5) + 3x * (-1 + 4x)) = 0
((-5 + 20x) + 3x * (-1 + 4x)) = 0
(-5 + 20x + (-1 * 3x + 4x * 3x)) = 0
(-5 + 20x + (-3x + 12x2)) = 0

Combine like terms: 20x + -3x = 17x
(-5 + 17x + 12x2) = 0

Solving
-5 + 17x + 12x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-5 + -3x)(1 + -4x) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(1 + -4x)' equal to zero and attempt to solve: Simplifying 1 + -4x = 0 Solving 1 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4x = 0 + -1 -4x = 0 + -1 Combine like terms: 0 + -1 = -1 -4x = -1 Divide each side by '-4'. x = 0.25 Simplifying x = 0.25

Solution

x = {-1.666666667, 0.25}

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