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

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


Simplifying
x(4 + x) = 7(x + -3 + 7)
(4 * x + x * x) = 7(x + -3 + 7)
(4x + x2) = 7(x + -3 + 7)

Reorder the terms:
4x + x2 = 7(-3 + 7 + x)

Combine like terms: -3 + 7 = 4
4x + x2 = 7(4 + x)
4x + x2 = (4 * 7 + x * 7)
4x + x2 = (28 + 7x)

Solving
4x + x2 = 28 + 7x

Solving for variable 'x'.

Reorder the terms:
-28 + 4x + -7x + x2 = 28 + 7x + -28 + -7x

Combine like terms: 4x + -7x = -3x
-28 + -3x + x2 = 28 + 7x + -28 + -7x

Reorder the terms:
-28 + -3x + x2 = 28 + -28 + 7x + -7x

Combine like terms: 28 + -28 = 0
-28 + -3x + x2 = 0 + 7x + -7x
-28 + -3x + x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-28 + -3x + x2 = 0

Factor a trinomial.
(-4 + -1x)(7 + -1x) = 0


Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 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 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-4, 7}

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