8x^2+18x+17=-x^2+77x+45

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Solution for 8x^2+18x+17=-x^2+77x+45 equation: 


Simplifying
8x2 + 18x + 17 = -1x2 + 77x + 45

Reorder the terms:
17 + 18x + 8x2 = -1x2 + 77x + 45

Reorder the terms:
17 + 18x + 8x2 = 45 + 77x + -1x2

Solving
17 + 18x + 8x2 = 45 + 77x + -1x2

Solving for variable 'x'.

Reorder the terms:
17 + -45 + 18x + -77x + 8x2 + x2 = 45 + 77x + -1x2 + -45 + -77x + x2

Combine like terms: 17 + -45 = -28
-28 + 18x + -77x + 8x2 + x2 = 45 + 77x + -1x2 + -45 + -77x + x2

Combine like terms: 18x + -77x = -59x
-28 + -59x + 8x2 + x2 = 45 + 77x + -1x2 + -45 + -77x + x2

Combine like terms: 8x2 + x2 = 9x2
-28 + -59x + 9x2 = 45 + 77x + -1x2 + -45 + -77x + x2

Reorder the terms:
-28 + -59x + 9x2 = 45 + -45 + 77x + -77x + -1x2 + x2

Combine like terms: 45 + -45 = 0
-28 + -59x + 9x2 = 0 + 77x + -77x + -1x2 + x2
-28 + -59x + 9x2 = 77x + -77x + -1x2 + x2

Combine like terms: 77x + -77x = 0
-28 + -59x + 9x2 = 0 + -1x2 + x2
-28 + -59x + 9x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-28 + -59x + 9x2 = 0

Factor a trinomial.
(-4 + -9x)(7 + -1x) = 0


Subproblem 1
Set the factor '(-4 + -9x)' equal to zero and attempt to solve:

Simplifying
-4 + -9x = 0

Solving
-4 + -9x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -9x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -9x = 0 + 4
-9x = 0 + 4

Combine like terms: 0 + 4 = 4
-9x = 4

Divide each side by '-9'.
x = -0.4444444444

Simplifying
x = -0.4444444444

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-0.4444444444, 7}

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