6x^2=63x+195

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Solution for 6x^2=63x+195 equation:


Simplifying
6x2 = 63x + 195

Reorder the terms:
6x2 = 195 + 63x

Solving
6x2 = 195 + 63x

Solving for variable 'x'.

Reorder the terms:
-195 + -63x + 6x2 = 195 + 63x + -195 + -63x

Reorder the terms:
-195 + -63x + 6x2 = 195 + -195 + 63x + -63x

Combine like terms: 195 + -195 = 0
-195 + -63x + 6x2 = 0 + 63x + -63x
-195 + -63x + 6x2 = 63x + -63x

Combine like terms: 63x + -63x = 0
-195 + -63x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-65 + -21x + 2x2) = 0

Factor a trinomial.
3((-5 + -2x)(13 + -1x)) = 0

Ignore the factor 3.

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 '(13 + -1x)' equal to zero and attempt to solve: Simplifying 13 + -1x = 0 Solving 13 + -1x = 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 + -1x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -1x = 0 + -13 -1x = 0 + -13 Combine like terms: 0 + -13 = -13 -1x = -13 Divide each side by '-1'. x = 13 Simplifying x = 13

Solution

x = {-2.5, 13}

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