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

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


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

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

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

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

Combine like terms: -5x + 12x = 7x
(-15 + 7x + 4x2) = 0

Solving
-15 + 7x + 4x2 = 0

Solving for variable 'x'.

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

Subproblem 1

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

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 = {-3, 1.25}

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