x^2-2x-7=-x^2+3x+5

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Solution for x^2-2x-7=-x^2+3x+5 equation: 


Simplifying
x2 + -2x + -7 = -1x2 + 3x + 5

Reorder the terms:
-7 + -2x + x2 = -1x2 + 3x + 5

Reorder the terms:
-7 + -2x + x2 = 5 + 3x + -1x2

Solving
-7 + -2x + x2 = 5 + 3x + -1x2

Solving for variable 'x'.

Reorder the terms:
-7 + -5 + -2x + -3x + x2 + x2 = 5 + 3x + -1x2 + -5 + -3x + x2

Combine like terms: -7 + -5 = -12
-12 + -2x + -3x + x2 + x2 = 5 + 3x + -1x2 + -5 + -3x + x2

Combine like terms: -2x + -3x = -5x
-12 + -5x + x2 + x2 = 5 + 3x + -1x2 + -5 + -3x + x2

Combine like terms: x2 + x2 = 2x2
-12 + -5x + 2x2 = 5 + 3x + -1x2 + -5 + -3x + x2

Reorder the terms:
-12 + -5x + 2x2 = 5 + -5 + 3x + -3x + -1x2 + x2

Combine like terms: 5 + -5 = 0
-12 + -5x + 2x2 = 0 + 3x + -3x + -1x2 + x2
-12 + -5x + 2x2 = 3x + -3x + -1x2 + x2

Combine like terms: 3x + -3x = 0
-12 + -5x + 2x2 = 0 + -1x2 + x2
-12 + -5x + 2x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-12 + -5x + 2x2 = 0

Factor a trinomial.
(-3 + -2x)(4 + -1x) = 0


Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve:

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 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 + -2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2x = 0 + 3
-2x = 0 + 3

Combine like terms: 0 + 3 = 3
-2x = 3

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5

Subproblem 2
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
Solution
x = {-1.5, 4}

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