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

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


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

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

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

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

Solving for variable 'x'.

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

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

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

Combine like terms: 4 + -4 = 0
-4 + -8x + 5x2 = 0 + 3x + -3x
-4 + -8x + 5x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-4 + -8x + 5x2 = 0

Factor a trinomial.
(-2 + -5x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-2 + -5x)' equal to zero and attempt to solve:

Simplifying
-2 + -5x = 0

Solving
-2 + -5x = 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 + -5x = 0 + 2

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

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

Divide each side by '-5'.
x = -0.4

Simplifying
x = -0.4

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 = {-0.4, 2}

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