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

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


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

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

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

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

Combine like terms: 20x + 3x = 23x
(12 + 23x + 5x2) = 22

Solving
12 + 23x + 5x2 = 22

Solving for variable 'x'.

Reorder the terms:
12 + -22 + 23x + 5x2 = 22 + -22

Combine like terms: 12 + -22 = -10
-10 + 23x + 5x2 = 22 + -22

Combine like terms: 22 + -22 = 0
-10 + 23x + 5x2 = 0

Factor a trinomial.
(-5 + -1x)(2 + -5x) = 0


Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 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 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5

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 = {-5, 0.4}

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