7x^2+17x-24=12-2x

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Solution for 7x^2+17x-24=12-2x equation: 


Simplifying
7x2 + 17x + -24 = 12 + -2x

Reorder the terms:
-24 + 17x + 7x2 = 12 + -2x

Solving
-24 + 17x + 7x2 = 12 + -2x

Solving for variable 'x'.

Reorder the terms:
-24 + -12 + 17x + 2x + 7x2 = 12 + -2x + -12 + 2x

Combine like terms: -24 + -12 = -36
-36 + 17x + 2x + 7x2 = 12 + -2x + -12 + 2x

Combine like terms: 17x + 2x = 19x
-36 + 19x + 7x2 = 12 + -2x + -12 + 2x

Reorder the terms:
-36 + 19x + 7x2 = 12 + -12 + -2x + 2x

Combine like terms: 12 + -12 = 0
-36 + 19x + 7x2 = 0 + -2x + 2x
-36 + 19x + 7x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
-36 + 19x + 7x2 = 0

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


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

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 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 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

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 = {-4, 1.285714286}

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