4x^2-65=7x

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Solution for 4x^2-65=7x equation:


Simplifying
4x2 + -65 = 7x

Reorder the terms:
-65 + 4x2 = 7x

Solving
-65 + 4x2 = 7x

Solving for variable 'x'.

Reorder the terms:
-65 + -7x + 4x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-65 + -7x + 4x2 = 0

Factor a trinomial.
(-13 + -4x)(5 + -1x) = 0

Subproblem 1

Set the factor '(-13 + -4x)' equal to zero and attempt to solve: Simplifying -13 + -4x = 0 Solving -13 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + -4x = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -4x = 0 + 13 -4x = 0 + 13 Combine like terms: 0 + 13 = 13 -4x = 13 Divide each side by '-4'. x = -3.25 Simplifying x = -3.25

Subproblem 2

Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5

Solution

x = {-3.25, 5}

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