3x(x+2)-1=x+7

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Solution for 3x(x+2)-1=x+7 equation: 


Simplifying
3x(x + 2) + -1 = x + 7

Reorder the terms:
3x(2 + x) + -1 = x + 7
(2 * 3x + x * 3x) + -1 = x + 7
(6x + 3x2) + -1 = x + 7

Reorder the terms:
-1 + 6x + 3x2 = x + 7

Reorder the terms:
-1 + 6x + 3x2 = 7 + x

Solving
-1 + 6x + 3x2 = 7 + x

Solving for variable 'x'.

Reorder the terms:
-1 + -7 + 6x + -1x + 3x2 = 7 + x + -7 + -1x

Combine like terms: -1 + -7 = -8
-8 + 6x + -1x + 3x2 = 7 + x + -7 + -1x

Combine like terms: 6x + -1x = 5x
-8 + 5x + 3x2 = 7 + x + -7 + -1x

Reorder the terms:
-8 + 5x + 3x2 = 7 + -7 + x + -1x

Combine like terms: 7 + -7 = 0
-8 + 5x + 3x2 = 0 + x + -1x
-8 + 5x + 3x2 = x + -1x

Combine like terms: x + -1x = 0
-8 + 5x + 3x2 = 0

Factor a trinomial.
(-8 + -3x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-8 + -3x)' equal to zero and attempt to solve:

Simplifying
-8 + -3x = 0

Solving
-8 + -3x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -3x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -3x = 0 + 8
-3x = 0 + 8

Combine like terms: 0 + 8 = 8
-3x = 8

Divide each side by '-3'.
x = -2.666666667

Simplifying
x = -2.666666667

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 = {-2.666666667, 1}

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