12g^2-76g+64=0

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Solution for 12g^2-76g+64=0 equation:


Simplifying
12g2 + -76g + 64 = 0

Reorder the terms:
64 + -76g + 12g2 = 0

Solving
64 + -76g + 12g2 = 0

Solving for variable 'g'.

Factor out the Greatest Common Factor (GCF), '4'.
4(16 + -19g + 3g2) = 0

Factor a trinomial.
4((1 + -1g)(16 + -3g)) = 0

Ignore the factor 4.

Subproblem 1

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

Subproblem 2

Set the factor '(16 + -3g)' equal to zero and attempt to solve: Simplifying 16 + -3g = 0 Solving 16 + -3g = 0 Move all terms containing g to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + -3g = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -3g = 0 + -16 -3g = 0 + -16 Combine like terms: 0 + -16 = -16 -3g = -16 Divide each side by '-3'. g = 5.333333333 Simplifying g = 5.333333333

Solution

g = {1, 5.333333333}

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