(-2x^2+5x-4)-(-4x+5)=0

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Solution for (-2x^2+5x-4)-(-4x+5)=0 equation: 


Simplifying
(-2x2 + 5x + -4) + -1(-4x + 5) = 0

Reorder the terms:
(-4 + 5x + -2x2) + -1(-4x + 5) = 0

Remove parenthesis around (-4 + 5x + -2x2)
-4 + 5x + -2x2 + -1(-4x + 5) = 0

Reorder the terms:
-4 + 5x + -2x2 + -1(5 + -4x) = 0
-4 + 5x + -2x2 + (5 * -1 + -4x * -1) = 0
-4 + 5x + -2x2 + (-5 + 4x) = 0

Reorder the terms:
-4 + -5 + 5x + 4x + -2x2 = 0

Combine like terms: -4 + -5 = -9
-9 + 5x + 4x + -2x2 = 0

Combine like terms: 5x + 4x = 9x
-9 + 9x + -2x2 = 0

Solving
-9 + 9x + -2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-3 + x)(3 + -2x) = 0


Subproblem 1
Set the factor '(-3 + x)' equal to zero and attempt to solve:

Simplifying
-3 + x = 0

Solving
-3 + x = 0

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

Add '3' to each side of the equation.
-3 + 3 + x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + x = 0 + 3
x = 0 + 3

Combine like terms: 0 + 3 = 3
x = 3

Simplifying
x = 3

Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

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

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

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {3, 1.5}

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