(4x+5)(3x-5)=-22

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Solution for (4x+5)(3x-5)=-22 equation: 


Simplifying
(4x + 5)(3x + -5) = -22

Reorder the terms:
(5 + 4x)(3x + -5) = -22

Reorder the terms:
(5 + 4x)(-5 + 3x) = -22

Multiply (5 + 4x) * (-5 + 3x)
(5(-5 + 3x) + 4x * (-5 + 3x)) = -22
((-5 * 5 + 3x * 5) + 4x * (-5 + 3x)) = -22
((-25 + 15x) + 4x * (-5 + 3x)) = -22
(-25 + 15x + (-5 * 4x + 3x * 4x)) = -22
(-25 + 15x + (-20x + 12x2)) = -22

Combine like terms: 15x + -20x = -5x
(-25 + -5x + 12x2) = -22

Solving
-25 + -5x + 12x2 = -22

Solving for variable 'x'.

Reorder the terms:
-25 + 22 + -5x + 12x2 = -22 + 22

Combine like terms: -25 + 22 = -3
-3 + -5x + 12x2 = -22 + 22

Combine like terms: -22 + 22 = 0
-3 + -5x + 12x2 = 0

Factor a trinomial.
(-1 + -3x)(3 + -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 '(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
Solution
x = {-0.3333333333, 0.75}

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