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

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


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

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

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

Add '-7' to each side of the equation.
7 + -5x + -7 + 2x2 = 7 + -7 + 3x

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

Combine like terms: 7 + -7 = 0
0 + -5x + 2x2 = 7 + -7 + 3x
-5x + 2x2 = 7 + -7 + 3x

Combine like terms: 7 + -7 = 0
-5x + 2x2 = 0 + 3x
-5x + 2x2 = 3x

Solving
-5x + 2x2 = 3x

Solving for variable 'x'.

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

Combine like terms: -5x + -3x = -8x
-8x + 2x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-8x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-4 + 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 '(-4 + x)' equal to zero and attempt to solve:

Simplifying
-4 + x = 0

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

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

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

Simplifying
x = 4
Solution
x = {0, 4}

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