0=4x^2-12x+5

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Solution for 0=4x^2-12x+5 equation:


Simplifying
0 = 4x2 + -12x + 5

Reorder the terms:
0 = 5 + -12x + 4x2

Solving
0 = 5 + -12x + 4x2

Solving for variable 'x'.

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

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

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

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

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

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

Subproblem 1

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

Subproblem 2

Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5

Solution

x = {2.5, 0.5}

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