4(x+5)=16x+4(x^2+7)

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Solution for 4(x+5)=16x+4(x^2+7) equation: 


Simplifying
4(x + 5) = 16x + 4(x2 + 7)

Reorder the terms:
4(5 + x) = 16x + 4(x2 + 7)
(5 * 4 + x * 4) = 16x + 4(x2 + 7)
(20 + 4x) = 16x + 4(x2 + 7)

Reorder the terms:
20 + 4x = 16x + 4(7 + x2)
20 + 4x = 16x + (7 * 4 + x2 * 4)
20 + 4x = 16x + (28 + 4x2)

Reorder the terms:
20 + 4x = 28 + 16x + 4x2

Solving
20 + 4x = 28 + 16x + 4x2

Solving for variable 'x'.

Reorder the terms:
20 + -28 + 4x + -16x + -4x2 = 28 + 16x + 4x2 + -28 + -16x + -4x2

Combine like terms: 20 + -28 = -8
-8 + 4x + -16x + -4x2 = 28 + 16x + 4x2 + -28 + -16x + -4x2

Combine like terms: 4x + -16x = -12x
-8 + -12x + -4x2 = 28 + 16x + 4x2 + -28 + -16x + -4x2

Reorder the terms:
-8 + -12x + -4x2 = 28 + -28 + 16x + -16x + 4x2 + -4x2

Combine like terms: 28 + -28 = 0
-8 + -12x + -4x2 = 0 + 16x + -16x + 4x2 + -4x2
-8 + -12x + -4x2 = 16x + -16x + 4x2 + -4x2

Combine like terms: 16x + -16x = 0
-8 + -12x + -4x2 = 0 + 4x2 + -4x2
-8 + -12x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-8 + -12x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '-4'.
-4(2 + 3x + x2) = 0

Factor a trinomial.
-4((2 + x)(1 + x)) = 0

Ignore the factor -4.

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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

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

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

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

Simplifying
x = -2

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

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {-2, -1}

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