(4x+5)(x-4)=-20x-22

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Solution for (4x+5)(x-4)=-20x-22 equation: 


Simplifying
(4x + 5)(x + -4) = -20x + -22

Reorder the terms:
(5 + 4x)(x + -4) = -20x + -22

Reorder the terms:
(5 + 4x)(-4 + x) = -20x + -22

Multiply (5 + 4x) * (-4 + x)
(5(-4 + x) + 4x * (-4 + x)) = -20x + -22
((-4 * 5 + x * 5) + 4x * (-4 + x)) = -20x + -22
((-20 + 5x) + 4x * (-4 + x)) = -20x + -22
(-20 + 5x + (-4 * 4x + x * 4x)) = -20x + -22
(-20 + 5x + (-16x + 4x2)) = -20x + -22

Combine like terms: 5x + -16x = -11x
(-20 + -11x + 4x2) = -20x + -22

Reorder the terms:
-20 + -11x + 4x2 = -22 + -20x

Solving
-20 + -11x + 4x2 = -22 + -20x

Solving for variable 'x'.

Reorder the terms:
-20 + 22 + -11x + 20x + 4x2 = -22 + -20x + 22 + 20x

Combine like terms: -20 + 22 = 2
2 + -11x + 20x + 4x2 = -22 + -20x + 22 + 20x

Combine like terms: -11x + 20x = 9x
2 + 9x + 4x2 = -22 + -20x + 22 + 20x

Reorder the terms:
2 + 9x + 4x2 = -22 + 22 + -20x + 20x

Combine like terms: -22 + 22 = 0
2 + 9x + 4x2 = 0 + -20x + 20x
2 + 9x + 4x2 = -20x + 20x

Combine like terms: -20x + 20x = 0
2 + 9x + 4x2 = 0

Factor a trinomial.
(2 + x)(1 + 4x) = 0


Subproblem 1
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2

Subproblem 2
Set the factor '(1 + 4x)' equal to zero and attempt to solve:

Simplifying
1 + 4x = 0

Solving
1 + 4x = 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 + 4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4x = 0 + -1
4x = 0 + -1

Combine like terms: 0 + -1 = -1
4x = -1

Divide each side by '4'.
x = -0.25

Simplifying
x = -0.25
Solution
x = {-2, -0.25}

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