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

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


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

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

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

Multiply (-5 + 4x) * (1 + 3x)
(-5(1 + 3x) + 4x * (1 + 3x)) = 0
((1 * -5 + 3x * -5) + 4x * (1 + 3x)) = 0
((-5 + -15x) + 4x * (1 + 3x)) = 0
(-5 + -15x + (1 * 4x + 3x * 4x)) = 0
(-5 + -15x + (4x + 12x2)) = 0

Combine like terms: -15x + 4x = -11x
(-5 + -11x + 12x2) = 0

Solving
-5 + -11x + 12x2 = 0

Solving for variable 'x'.

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

Subproblem 1

Set the factor '(-1 + -3x)' equal to zero and attempt to solve: Simplifying -1 + -3x = 0 Solving -1 + -3x = 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 + -3x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3x = 0 + 1 -3x = 0 + 1 Combine like terms: 0 + 1 = 1 -3x = 1 Divide each side by '-3'. x = -0.3333333333 Simplifying x = -0.3333333333

Subproblem 2

Set the factor '(5 + -4x)' equal to zero and attempt to solve: Simplifying 5 + -4x = 0 Solving 5 + -4x = 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 + -4x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4x = 0 + -5 -4x = 0 + -5 Combine like terms: 0 + -5 = -5 -4x = -5 Divide each side by '-4'. x = 1.25 Simplifying x = 1.25

Solution

x = {-0.3333333333, 1.25}

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