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

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


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

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

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

Reorder the terms:
2x + 2x2 = 7 + -2x + -1x2

Solving
2x + 2x2 = 7 + -2x + -1x2

Solving for variable 'x'.

Reorder the terms:
-7 + 2x + 2x + 2x2 + x2 = 7 + -2x + -1x2 + -7 + 2x + x2

Combine like terms: 2x + 2x = 4x
-7 + 4x + 2x2 + x2 = 7 + -2x + -1x2 + -7 + 2x + x2

Combine like terms: 2x2 + x2 = 3x2
-7 + 4x + 3x2 = 7 + -2x + -1x2 + -7 + 2x + x2

Reorder the terms:
-7 + 4x + 3x2 = 7 + -7 + -2x + 2x + -1x2 + x2

Combine like terms: 7 + -7 = 0
-7 + 4x + 3x2 = 0 + -2x + 2x + -1x2 + x2
-7 + 4x + 3x2 = -2x + 2x + -1x2 + x2

Combine like terms: -2x + 2x = 0
-7 + 4x + 3x2 = 0 + -1x2 + x2
-7 + 4x + 3x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-7 + 4x + 3x2 = 0

Factor a trinomial.
(-7 + -3x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-7 + -3x)' equal to zero and attempt to solve:

Simplifying
-7 + -3x = 0

Solving
-7 + -3x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -3x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -3x = 0 + 7
-3x = 0 + 7

Combine like terms: 0 + 7 = 7
-3x = 7

Divide each side by '-3'.
x = -2.333333333

Simplifying
x = -2.333333333

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 = {-2.333333333, 1}

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