3x^2-5-4x=10x+65-3x

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Solution for 3x^2-5-4x=10x+65-3x equation:


Simplifying
3x2 + -5 + -4x = 10x + 65 + -3x

Reorder the terms:
-5 + -4x + 3x2 = 10x + 65 + -3x

Reorder the terms:
-5 + -4x + 3x2 = 65 + 10x + -3x

Combine like terms: 10x + -3x = 7x
-5 + -4x + 3x2 = 65 + 7x

Solving
-5 + -4x + 3x2 = 65 + 7x

Solving for variable 'x'.

Reorder the terms:
-5 + -65 + -4x + -7x + 3x2 = 65 + 7x + -65 + -7x

Combine like terms: -5 + -65 = -70
-70 + -4x + -7x + 3x2 = 65 + 7x + -65 + -7x

Combine like terms: -4x + -7x = -11x
-70 + -11x + 3x2 = 65 + 7x + -65 + -7x

Reorder the terms:
-70 + -11x + 3x2 = 65 + -65 + 7x + -7x

Combine like terms: 65 + -65 = 0
-70 + -11x + 3x2 = 0 + 7x + -7x
-70 + -11x + 3x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-70 + -11x + 3x2 = 0

Factor a trinomial.
(-10 + -3x)(7 + -1x) = 0

Subproblem 1

Set the factor '(-10 + -3x)' equal to zero and attempt to solve: Simplifying -10 + -3x = 0 Solving -10 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + -3x = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -3x = 0 + 10 -3x = 0 + 10 Combine like terms: 0 + 10 = 10 -3x = 10 Divide each side by '-3'. x = -3.333333333 Simplifying x = -3.333333333

Subproblem 2

Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7

Solution

x = {-3.333333333, 7}

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