7X^2+5X-7=17-8X

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Solution for 7X^2+5X-7=17-8X equation: 


Simplifying
7X2 + 5X + -7 = 17 + -8X

Reorder the terms:
-7 + 5X + 7X2 = 17 + -8X

Solving
-7 + 5X + 7X2 = 17 + -8X

Solving for variable 'X'.

Reorder the terms:
-7 + -17 + 5X + 8X + 7X2 = 17 + -8X + -17 + 8X

Combine like terms: -7 + -17 = -24
-24 + 5X + 8X + 7X2 = 17 + -8X + -17 + 8X

Combine like terms: 5X + 8X = 13X
-24 + 13X + 7X2 = 17 + -8X + -17 + 8X

Reorder the terms:
-24 + 13X + 7X2 = 17 + -17 + -8X + 8X

Combine like terms: 17 + -17 = 0
-24 + 13X + 7X2 = 0 + -8X + 8X
-24 + 13X + 7X2 = -8X + 8X

Combine like terms: -8X + 8X = 0
-24 + 13X + 7X2 = 0

Factor a trinomial.
(-3 + -1X)(8 + -7X) = 0


Subproblem 1
Set the factor '(-3 + -1X)' equal to zero and attempt to solve:

Simplifying
-3 + -1X = 0

Solving
-3 + -1X = 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 + -1X = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1X = 0 + 3
-1X = 0 + 3

Combine like terms: 0 + 3 = 3
-1X = 3

Divide each side by '-1'.
X = -3

Simplifying
X = -3

Subproblem 2
Set the factor '(8 + -7X)' equal to zero and attempt to solve:

Simplifying
8 + -7X = 0

Solving
8 + -7X = 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 + -7X = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -7X = 0 + -8
-7X = 0 + -8

Combine like terms: 0 + -8 = -8
-7X = -8

Divide each side by '-7'.
X = 1.142857143

Simplifying
X = 1.142857143
Solution
X = {-3, 1.142857143}

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