2x^2+3x-4=8x-4

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Solution for 2x^2+3x-4=8x-4 equation: 


Simplifying
2x2 + 3x + -4 = 8x + -4

Reorder the terms:
-4 + 3x + 2x2 = 8x + -4

Reorder the terms:
-4 + 3x + 2x2 = -4 + 8x

Add '4' to each side of the equation.
-4 + 3x + 4 + 2x2 = -4 + 4 + 8x

Reorder the terms:
-4 + 4 + 3x + 2x2 = -4 + 4 + 8x

Combine like terms: -4 + 4 = 0
0 + 3x + 2x2 = -4 + 4 + 8x
3x + 2x2 = -4 + 4 + 8x

Combine like terms: -4 + 4 = 0
3x + 2x2 = 0 + 8x
3x + 2x2 = 8x

Solving
3x + 2x2 = 8x

Solving for variable 'x'.

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

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

Combine like terms: 8x + -8x = 0
-5x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-5 + 2x) = 0


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 '(-5 + 2x)' equal to zero and attempt to solve:

Simplifying
-5 + 2x = 0

Solving
-5 + 2x = 0

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

Add '5' to each side of the equation.
-5 + 5 + 2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 2x = 0 + 5
2x = 0 + 5

Combine like terms: 0 + 5 = 5
2x = 5

Divide each side by '2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {0, 2.5}

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