4x^2-6=5x

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Solution for 4x^2-6=5x equation:


Simplifying
4x2 + -6 = 5x

Reorder the terms:
-6 + 4x2 = 5x

Solving
-6 + 4x2 = 5x

Solving for variable 'x'.

Reorder the terms:
-6 + -5x + 4x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-6 + -5x + 4x2 = 0

Factor a trinomial.
(-3 + -4x)(2 + -1x) = 0

Subproblem 1

Set the factor '(-3 + -4x)' equal to zero and attempt to solve: Simplifying -3 + -4x = 0 Solving -3 + -4x = 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 + -4x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4x = 0 + 3 -4x = 0 + 3 Combine like terms: 0 + 3 = 3 -4x = 3 Divide each side by '-4'. x = -0.75 Simplifying x = -0.75

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 = {-0.75, 2}

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