4x^2=27x+81

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Solution for 4x^2=27x+81 equation:


Simplifying
4x2 = 27x + 81

Reorder the terms:
4x2 = 81 + 27x

Solving
4x2 = 81 + 27x

Solving for variable 'x'.

Reorder the terms:
-81 + -27x + 4x2 = 81 + 27x + -81 + -27x

Reorder the terms:
-81 + -27x + 4x2 = 81 + -81 + 27x + -27x

Combine like terms: 81 + -81 = 0
-81 + -27x + 4x2 = 0 + 27x + -27x
-81 + -27x + 4x2 = 27x + -27x

Combine like terms: 27x + -27x = 0
-81 + -27x + 4x2 = 0

Factor a trinomial.
(-9 + -4x)(9 + -1x) = 0

Subproblem 1

Set the factor '(-9 + -4x)' equal to zero and attempt to solve: Simplifying -9 + -4x = 0 Solving -9 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -4x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -4x = 0 + 9 -4x = 0 + 9 Combine like terms: 0 + 9 = 9 -4x = 9 Divide each side by '-4'. x = -2.25 Simplifying x = -2.25

Subproblem 2

Set the factor '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9

Solution

x = {-2.25, 9}

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