3(x+1)x+4(x+3)=22

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


Simplifying
3(x + 1) * x + 4(x + 3) = 22

Reorder the terms:
3(1 + x) * x + 4(x + 3) = 22

Reorder the terms for easier multiplication:
3x(1 + x) + 4(x + 3) = 22
(1 * 3x + x * 3x) + 4(x + 3) = 22
(3x + 3x2) + 4(x + 3) = 22

Reorder the terms:
3x + 3x2 + 4(3 + x) = 22
3x + 3x2 + (3 * 4 + x * 4) = 22
3x + 3x2 + (12 + 4x) = 22

Reorder the terms:
12 + 3x + 4x + 3x2 = 22

Combine like terms: 3x + 4x = 7x
12 + 7x + 3x2 = 22

Solving
12 + 7x + 3x2 = 22

Solving for variable 'x'.

Reorder the terms:
12 + -22 + 7x + 3x2 = 22 + -22

Combine like terms: 12 + -22 = -10
-10 + 7x + 3x2 = 22 + -22

Combine like terms: 22 + -22 = 0
-10 + 7x + 3x2 = 0

Factor a trinomial.
(-10 + -3x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-10 + -3x)' equal to zero and attempt to solve:

Simplifying
-10 + -3x = 0

Solving
-10 + -3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '10' to each side of the equation.
-10 + 10 + -3x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -3x = 0 + 10
-3x = 0 + 10

Combine like terms: 0 + 10 = 10
-3x = 10

Divide each side by '-3'.
x = -3.333333333

Simplifying
x = -3.333333333

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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {-3.333333333, 1}

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