x(x+2)=4(5-x)+7

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Solution for x(x+2)=4(5-x)+7 equation: 


Simplifying
x(x + 2) = 4(5 + -1x) + 7

Reorder the terms:
x(2 + x) = 4(5 + -1x) + 7
(2 * x + x * x) = 4(5 + -1x) + 7
(2x + x2) = 4(5 + -1x) + 7
2x + x2 = (5 * 4 + -1x * 4) + 7
2x + x2 = (20 + -4x) + 7

Reorder the terms:
2x + x2 = 20 + 7 + -4x

Combine like terms: 20 + 7 = 27
2x + x2 = 27 + -4x

Solving
2x + x2 = 27 + -4x

Solving for variable 'x'.

Reorder the terms:
-27 + 2x + 4x + x2 = 27 + -4x + -27 + 4x

Combine like terms: 2x + 4x = 6x
-27 + 6x + x2 = 27 + -4x + -27 + 4x

Reorder the terms:
-27 + 6x + x2 = 27 + -27 + -4x + 4x

Combine like terms: 27 + -27 = 0
-27 + 6x + x2 = 0 + -4x + 4x
-27 + 6x + x2 = -4x + 4x

Combine like terms: -4x + 4x = 0
-27 + 6x + x2 = 0

Factor a trinomial.
(-9 + -1x)(3 + -1x) = 0


Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-9, 3}

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