7x^2+9x-10=17-3x

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Solution for 7x^2+9x-10=17-3x equation: 


Simplifying
7x2 + 9x + -10 = 17 + -3x

Reorder the terms:
-10 + 9x + 7x2 = 17 + -3x

Solving
-10 + 9x + 7x2 = 17 + -3x

Solving for variable 'x'.

Reorder the terms:
-10 + -17 + 9x + 3x + 7x2 = 17 + -3x + -17 + 3x

Combine like terms: -10 + -17 = -27
-27 + 9x + 3x + 7x2 = 17 + -3x + -17 + 3x

Combine like terms: 9x + 3x = 12x
-27 + 12x + 7x2 = 17 + -3x + -17 + 3x

Reorder the terms:
-27 + 12x + 7x2 = 17 + -17 + -3x + 3x

Combine like terms: 17 + -17 = 0
-27 + 12x + 7x2 = 0 + -3x + 3x
-27 + 12x + 7x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
-27 + 12x + 7x2 = 0

Factor a trinomial.
(-3 + -1x)(9 + -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 '(9 + -7x)' equal to zero and attempt to solve:

Simplifying
9 + -7x = 0

Solving
9 + -7x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -7x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -7x = 0 + -9
-7x = 0 + -9

Combine like terms: 0 + -9 = -9
-7x = -9

Divide each side by '-7'.
x = 1.285714286

Simplifying
x = 1.285714286
Solution
x = {-3, 1.285714286}

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