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

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


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

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

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

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

Combine like terms: 12x + -5x = 7x
(-3 + 7x + 20x2) = 3

Solving
-3 + 7x + 20x2 = 3

Solving for variable 'x'.

Reorder the terms:
-3 + -3 + 7x + 20x2 = 3 + -3

Combine like terms: -3 + -3 = -6
-6 + 7x + 20x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-6 + 7x + 20x2 = 0

Factor a trinomial.
(-3 + -4x)(2 + -5x) = 0

Subproblem 1

Set the factor '(-3 + -4x)' equal to zero and attempt to solve: Simplifying -3 + -4x = 0 Solving -3 + -4x = 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 + -4x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4x = 0 + 3 -4x = 0 + 3 Combine like terms: 0 + 3 = 3 -4x = 3 Divide each side by '-4'. x = -0.75 Simplifying x = -0.75

Subproblem 2

Set the factor '(2 + -5x)' equal to zero and attempt to solve: Simplifying 2 + -5x = 0 Solving 2 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -5x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5x = 0 + -2 -5x = 0 + -2 Combine like terms: 0 + -2 = -2 -5x = -2 Divide each side by '-5'. x = 0.4 Simplifying x = 0.4

Solution

x = {-0.75, 0.4}

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