3x^2=-84+33x

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Solution for 3x^2=-84+33x equation:


Simplifying
3x2 = -84 + 33x

Solving
3x2 = -84 + 33x

Solving for variable 'x'.

Reorder the terms:
84 + -33x + 3x2 = -84 + 33x + 84 + -33x

Reorder the terms:
84 + -33x + 3x2 = -84 + 84 + 33x + -33x

Combine like terms: -84 + 84 = 0
84 + -33x + 3x2 = 0 + 33x + -33x
84 + -33x + 3x2 = 33x + -33x

Combine like terms: 33x + -33x = 0
84 + -33x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(28 + -11x + x2) = 0

Factor a trinomial.
3((4 + -1x)(7 + -1x)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4

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 = {4, 7}

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