(x+7)*(x+7-3x+4)=0

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Solution for (x+7)*(x+7-3x+4)=0 equation: 


Simplifying
(x + 7)(x + 7 + -3x + 4) = 0

Reorder the terms:
(7 + x)(x + 7 + -3x + 4) = 0

Reorder the terms:
(7 + x)(7 + 4 + x + -3x) = 0

Combine like terms: 7 + 4 = 11
(7 + x)(11 + x + -3x) = 0

Combine like terms: x + -3x = -2x
(7 + x)(11 + -2x) = 0

Multiply (7 + x) * (11 + -2x)
(7(11 + -2x) + x(11 + -2x)) = 0
((11 * 7 + -2x * 7) + x(11 + -2x)) = 0
((77 + -14x) + x(11 + -2x)) = 0
(77 + -14x + (11 * x + -2x * x)) = 0
(77 + -14x + (11x + -2x2)) = 0

Combine like terms: -14x + 11x = -3x
(77 + -3x + -2x2) = 0

Solving
77 + -3x + -2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(11 + -2x)(7 + x) = 0


Subproblem 1
Set the factor '(11 + -2x)' equal to zero and attempt to solve:

Simplifying
11 + -2x = 0

Solving
11 + -2x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -2x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -2x = 0 + -11
-2x = 0 + -11

Combine like terms: 0 + -11 = -11
-2x = -11

Divide each side by '-2'.
x = 5.5

Simplifying
x = 5.5

Subproblem 2
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 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 + x = 0 + -7

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

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

Simplifying
x = -7
Solution
x = {5.5, -7}

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