4x^2+27x-14=10-2x

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Solution for 4x^2+27x-14=10-2x equation: 


Simplifying
4x2 + 27x + -14 = 10 + -2x

Reorder the terms:
-14 + 27x + 4x2 = 10 + -2x

Solving
-14 + 27x + 4x2 = 10 + -2x

Solving for variable 'x'.

Reorder the terms:
-14 + -10 + 27x + 2x + 4x2 = 10 + -2x + -10 + 2x

Combine like terms: -14 + -10 = -24
-24 + 27x + 2x + 4x2 = 10 + -2x + -10 + 2x

Combine like terms: 27x + 2x = 29x
-24 + 29x + 4x2 = 10 + -2x + -10 + 2x

Reorder the terms:
-24 + 29x + 4x2 = 10 + -10 + -2x + 2x

Combine like terms: 10 + -10 = 0
-24 + 29x + 4x2 = 0 + -2x + 2x
-24 + 29x + 4x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
-24 + 29x + 4x2 = 0

Factor a trinomial.
(-8 + -1x)(3 + -4x) = 0


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 '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4x = 0 + -3
-4x = 0 + -3

Combine like terms: 0 + -3 = -3
-4x = -3

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75
Solution
x = {-8, 0.75}

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