16x^2+10x-27=-6x+5

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Solution for 16x^2+10x-27=-6x+5 equation: 


Simplifying
16x2 + 10x + -27 = -6x + 5

Reorder the terms:
-27 + 10x + 16x2 = -6x + 5

Reorder the terms:
-27 + 10x + 16x2 = 5 + -6x

Solving
-27 + 10x + 16x2 = 5 + -6x

Solving for variable 'x'.

Reorder the terms:
-27 + -5 + 10x + 6x + 16x2 = 5 + -6x + -5 + 6x

Combine like terms: -27 + -5 = -32
-32 + 10x + 6x + 16x2 = 5 + -6x + -5 + 6x

Combine like terms: 10x + 6x = 16x
-32 + 16x + 16x2 = 5 + -6x + -5 + 6x

Reorder the terms:
-32 + 16x + 16x2 = 5 + -5 + -6x + 6x

Combine like terms: 5 + -5 = 0
-32 + 16x + 16x2 = 0 + -6x + 6x
-32 + 16x + 16x2 = -6x + 6x

Combine like terms: -6x + 6x = 0
-32 + 16x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(-2 + x + x2) = 0

Factor a trinomial.
16((-2 + -1x)(1 + -1x)) = 0

Ignore the factor 16.

Subproblem 1
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

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 = {-2, 1}

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