4x^2-3x+7=2x^2+x+7

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Solution for 4x^2-3x+7=2x^2+x+7 equation: 


Simplifying
4x2 + -3x + 7 = 2x2 + x + 7

Reorder the terms:
7 + -3x + 4x2 = 2x2 + x + 7

Reorder the terms:
7 + -3x + 4x2 = 7 + x + 2x2

Add '-7' to each side of the equation.
7 + -3x + -7 + 4x2 = 7 + x + -7 + 2x2

Reorder the terms:
7 + -7 + -3x + 4x2 = 7 + x + -7 + 2x2

Combine like terms: 7 + -7 = 0
0 + -3x + 4x2 = 7 + x + -7 + 2x2
-3x + 4x2 = 7 + x + -7 + 2x2

Reorder the terms:
-3x + 4x2 = 7 + -7 + x + 2x2

Combine like terms: 7 + -7 = 0
-3x + 4x2 = 0 + x + 2x2
-3x + 4x2 = x + 2x2

Solving
-3x + 4x2 = x + 2x2

Solving for variable 'x'.

Reorder the terms:
-3x + -1x + 4x2 + -2x2 = x + 2x2 + -1x + -2x2

Combine like terms: -3x + -1x = -4x
-4x + 4x2 + -2x2 = x + 2x2 + -1x + -2x2

Combine like terms: 4x2 + -2x2 = 2x2
-4x + 2x2 = x + 2x2 + -1x + -2x2

Reorder the terms:
-4x + 2x2 = x + -1x + 2x2 + -2x2

Combine like terms: x + -1x = 0
-4x + 2x2 = 0 + 2x2 + -2x2
-4x + 2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-2 + x) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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

Simplifying
-2 + x = 0

Solving
-2 + x = 0

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

Add '2' to each side of the equation.
-2 + 2 + x = 0 + 2

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

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

Simplifying
x = 2
Solution
x = {0, 2}

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