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

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


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

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

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

Multiply (1 + 5x) * (-4 + 3x)
(1(-4 + 3x) + 5x * (-4 + 3x)) = 0
((-4 * 1 + 3x * 1) + 5x * (-4 + 3x)) = 0
((-4 + 3x) + 5x * (-4 + 3x)) = 0
(-4 + 3x + (-4 * 5x + 3x * 5x)) = 0
(-4 + 3x + (-20x + 15x2)) = 0

Combine like terms: 3x + -20x = -17x
(-4 + -17x + 15x2) = 0

Solving
-4 + -17x + 15x2 = 0

Solving for variable 'x'.

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

Subproblem 1

Set the factor '(-1 + -5x)' equal to zero and attempt to solve: Simplifying -1 + -5x = 0 Solving -1 + -5x = 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 + -5x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -5x = 0 + 1 -5x = 0 + 1 Combine like terms: 0 + 1 = 1 -5x = 1 Divide each side by '-5'. x = -0.2 Simplifying x = -0.2

Subproblem 2

Set the factor '(4 + -3x)' equal to zero and attempt to solve: Simplifying 4 + -3x = 0 Solving 4 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3x = 0 + -4 -3x = 0 + -4 Combine like terms: 0 + -4 = -4 -3x = -4 Divide each side by '-3'. x = 1.333333333 Simplifying x = 1.333333333

Solution

x = {-0.2, 1.333333333}

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