4x^2-8x+3=4x-5

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Solution for 4x^2-8x+3=4x-5 equation: 


Simplifying
4x2 + -8x + 3 = 4x + -5

Reorder the terms:
3 + -8x + 4x2 = 4x + -5

Reorder the terms:
3 + -8x + 4x2 = -5 + 4x

Solving
3 + -8x + 4x2 = -5 + 4x

Solving for variable 'x'.

Reorder the terms:
3 + 5 + -8x + -4x + 4x2 = -5 + 4x + 5 + -4x

Combine like terms: 3 + 5 = 8
8 + -8x + -4x + 4x2 = -5 + 4x + 5 + -4x

Combine like terms: -8x + -4x = -12x
8 + -12x + 4x2 = -5 + 4x + 5 + -4x

Reorder the terms:
8 + -12x + 4x2 = -5 + 5 + 4x + -4x

Combine like terms: -5 + 5 = 0
8 + -12x + 4x2 = 0 + 4x + -4x
8 + -12x + 4x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
8 + -12x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(2 + -3x + x2) = 0

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

Ignore the factor 4.

Subproblem 1
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

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {1, 2}

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