16x^2+217=-7+8x^2-88x

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Solution for 16x^2+217=-7+8x^2-88x equation: 


Simplifying
16x2 + 217 = -7 + 8x2 + -88x

Reorder the terms:
217 + 16x2 = -7 + 8x2 + -88x

Reorder the terms:
217 + 16x2 = -7 + -88x + 8x2

Solving
217 + 16x2 = -7 + -88x + 8x2

Solving for variable 'x'.

Reorder the terms:
217 + 7 + 88x + 16x2 + -8x2 = -7 + -88x + 8x2 + 7 + 88x + -8x2

Combine like terms: 217 + 7 = 224
224 + 88x + 16x2 + -8x2 = -7 + -88x + 8x2 + 7 + 88x + -8x2

Combine like terms: 16x2 + -8x2 = 8x2
224 + 88x + 8x2 = -7 + -88x + 8x2 + 7 + 88x + -8x2

Reorder the terms:
224 + 88x + 8x2 = -7 + 7 + -88x + 88x + 8x2 + -8x2

Combine like terms: -7 + 7 = 0
224 + 88x + 8x2 = 0 + -88x + 88x + 8x2 + -8x2
224 + 88x + 8x2 = -88x + 88x + 8x2 + -8x2

Combine like terms: -88x + 88x = 0
224 + 88x + 8x2 = 0 + 8x2 + -8x2
224 + 88x + 8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
224 + 88x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(28 + 11x + x2) = 0

Factor a trinomial.
8((7 + x)(4 + x)) = 0

Ignore the factor 8.

Subproblem 1
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

Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 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 + x = 0 + -4

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

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

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

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