(x+1)(2x+3)=4x^2-22

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Solution for (x+1)(2x+3)=4x^2-22 equation: 


Simplifying
(x + 1)(2x + 3) = 4x2 + -22

Reorder the terms:
(1 + x)(2x + 3) = 4x2 + -22

Reorder the terms:
(1 + x)(3 + 2x) = 4x2 + -22

Multiply (1 + x) * (3 + 2x)
(1(3 + 2x) + x(3 + 2x)) = 4x2 + -22
((3 * 1 + 2x * 1) + x(3 + 2x)) = 4x2 + -22
((3 + 2x) + x(3 + 2x)) = 4x2 + -22
(3 + 2x + (3 * x + 2x * x)) = 4x2 + -22
(3 + 2x + (3x + 2x2)) = 4x2 + -22

Combine like terms: 2x + 3x = 5x
(3 + 5x + 2x2) = 4x2 + -22

Reorder the terms:
3 + 5x + 2x2 = -22 + 4x2

Solving
3 + 5x + 2x2 = -22 + 4x2

Solving for variable 'x'.

Reorder the terms:
3 + 22 + 5x + 2x2 + -4x2 = -22 + 4x2 + 22 + -4x2

Combine like terms: 3 + 22 = 25
25 + 5x + 2x2 + -4x2 = -22 + 4x2 + 22 + -4x2

Combine like terms: 2x2 + -4x2 = -2x2
25 + 5x + -2x2 = -22 + 4x2 + 22 + -4x2

Reorder the terms:
25 + 5x + -2x2 = -22 + 22 + 4x2 + -4x2

Combine like terms: -22 + 22 = 0
25 + 5x + -2x2 = 0 + 4x2 + -4x2
25 + 5x + -2x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
25 + 5x + -2x2 = 0

Factor a trinomial.
(5 + -1x)(5 + 2x) = 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 '(5 + 2x)' equal to zero and attempt to solve:

Simplifying
5 + 2x = 0

Solving
5 + 2x = 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 + 2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2x = 0 + -5
2x = 0 + -5

Combine like terms: 0 + -5 = -5
2x = -5

Divide each side by '2'.
x = -2.5

Simplifying
x = -2.5
Solution
x = {5, -2.5}

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