2-2x=2x^2+5x-7

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Solution for 2-2x=2x^2+5x-7 equation: 


Simplifying
2 + -2x = 2x2 + 5x + -7

Reorder the terms:
2 + -2x = -7 + 5x + 2x2

Solving
2 + -2x = -7 + 5x + 2x2

Solving for variable 'x'.

Reorder the terms:
2 + 7 + -2x + -5x + -2x2 = -7 + 5x + 2x2 + 7 + -5x + -2x2

Combine like terms: 2 + 7 = 9
9 + -2x + -5x + -2x2 = -7 + 5x + 2x2 + 7 + -5x + -2x2

Combine like terms: -2x + -5x = -7x
9 + -7x + -2x2 = -7 + 5x + 2x2 + 7 + -5x + -2x2

Reorder the terms:
9 + -7x + -2x2 = -7 + 7 + 5x + -5x + 2x2 + -2x2

Combine like terms: -7 + 7 = 0
9 + -7x + -2x2 = 0 + 5x + -5x + 2x2 + -2x2
9 + -7x + -2x2 = 5x + -5x + 2x2 + -2x2

Combine like terms: 5x + -5x = 0
9 + -7x + -2x2 = 0 + 2x2 + -2x2
9 + -7x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
9 + -7x + -2x2 = 0

Factor a trinomial.
(1 + -1x)(9 + 2x) = 0


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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1

Subproblem 2
Set the factor '(9 + 2x)' equal to zero and attempt to solve:

Simplifying
9 + 2x = 0

Solving
9 + 2x = 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 + 2x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 2x = 0 + -9
2x = 0 + -9

Combine like terms: 0 + -9 = -9
2x = -9

Divide each side by '2'.
x = -4.5

Simplifying
x = -4.5
Solution
x = {1, -4.5}

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