4x^2+10x-8=17-5x

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Solution for 4x^2+10x-8=17-5x equation: 


Simplifying
4x2 + 10x + -8 = 17 + -5x

Reorder the terms:
-8 + 10x + 4x2 = 17 + -5x

Solving
-8 + 10x + 4x2 = 17 + -5x

Solving for variable 'x'.

Reorder the terms:
-8 + -17 + 10x + 5x + 4x2 = 17 + -5x + -17 + 5x

Combine like terms: -8 + -17 = -25
-25 + 10x + 5x + 4x2 = 17 + -5x + -17 + 5x

Combine like terms: 10x + 5x = 15x
-25 + 15x + 4x2 = 17 + -5x + -17 + 5x

Reorder the terms:
-25 + 15x + 4x2 = 17 + -17 + -5x + 5x

Combine like terms: 17 + -17 = 0
-25 + 15x + 4x2 = 0 + -5x + 5x
-25 + 15x + 4x2 = -5x + 5x

Combine like terms: -5x + 5x = 0
-25 + 15x + 4x2 = 0

Factor a trinomial.
(-5 + -1x)(5 + -4x) = 0


Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5

Subproblem 2
Set the factor '(5 + -4x)' equal to zero and attempt to solve:

Simplifying
5 + -4x = 0

Solving
5 + -4x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4x = 0 + -5
-4x = 0 + -5

Combine like terms: 0 + -5 = -5
-4x = -5

Divide each side by '-4'.
x = 1.25

Simplifying
x = 1.25
Solution
x = {-5, 1.25}

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