27=35+4x-4x^2

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Solution for 27=35+4x-4x^2 equation: 


Simplifying
27 = 35 + 4x + -4x2

Solving
27 = 35 + 4x + -4x2

Solving for variable 'x'.

Combine like terms: 27 + -35 = -8
-8 + -4x + 4x2 = 35 + 4x + -4x2 + -35 + -4x + 4x2

Reorder the terms:
-8 + -4x + 4x2 = 35 + -35 + 4x + -4x + -4x2 + 4x2

Combine like terms: 35 + -35 = 0
-8 + -4x + 4x2 = 0 + 4x + -4x + -4x2 + 4x2
-8 + -4x + 4x2 = 4x + -4x + -4x2 + 4x2

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

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

Factor out the Greatest Common Factor (GCF), '4'.
4(-2 + -1x + x2) = 0

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

Ignore the factor 4.

Subproblem 1
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

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

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

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