4x(x+8)=32+4x

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Solution for 4x(x+8)=32+4x equation: 


Simplifying
4x(x + 8) = 32 + 4x

Reorder the terms:
4x(8 + x) = 32 + 4x
(8 * 4x + x * 4x) = 32 + 4x
(32x + 4x2) = 32 + 4x

Solving
32x + 4x2 = 32 + 4x

Solving for variable 'x'.

Reorder the terms:
-32 + 32x + -4x + 4x2 = 32 + 4x + -32 + -4x

Combine like terms: 32x + -4x = 28x
-32 + 28x + 4x2 = 32 + 4x + -32 + -4x

Reorder the terms:
-32 + 28x + 4x2 = 32 + -32 + 4x + -4x

Combine like terms: 32 + -32 = 0
-32 + 28x + 4x2 = 0 + 4x + -4x
-32 + 28x + 4x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-32 + 28x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-8 + 7x + x2) = 0

Factor a trinomial.
4((-8 + -1x)(1 + -1x)) = 0

Ignore the factor 4.

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

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 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 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8

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 = {-8, 1}

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