3x^2+8x-7=x^2+x+2

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Solution for 3x^2+8x-7=x^2+x+2 equation: 


Simplifying
3x2 + 8x + -7 = x2 + x + 2

Reorder the terms:
-7 + 8x + 3x2 = x2 + x + 2

Reorder the terms:
-7 + 8x + 3x2 = 2 + x + x2

Solving
-7 + 8x + 3x2 = 2 + x + x2

Solving for variable 'x'.

Reorder the terms:
-7 + -2 + 8x + -1x + 3x2 + -1x2 = 2 + x + x2 + -2 + -1x + -1x2

Combine like terms: -7 + -2 = -9
-9 + 8x + -1x + 3x2 + -1x2 = 2 + x + x2 + -2 + -1x + -1x2

Combine like terms: 8x + -1x = 7x
-9 + 7x + 3x2 + -1x2 = 2 + x + x2 + -2 + -1x + -1x2

Combine like terms: 3x2 + -1x2 = 2x2
-9 + 7x + 2x2 = 2 + x + x2 + -2 + -1x + -1x2

Reorder the terms:
-9 + 7x + 2x2 = 2 + -2 + x + -1x + x2 + -1x2

Combine like terms: 2 + -2 = 0
-9 + 7x + 2x2 = 0 + x + -1x + x2 + -1x2
-9 + 7x + 2x2 = x + -1x + x2 + -1x2

Combine like terms: x + -1x = 0
-9 + 7x + 2x2 = 0 + x2 + -1x2
-9 + 7x + 2x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-9 + 7x + 2x2 = 0

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


Subproblem 1
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

Subproblem 2
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
Solution
x = {-4.5, 1}

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