log(7)(2x^2-16x)=log(7)(-60+x^2)

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Solution for log(7)(2x^2-16x)=log(7)(-60+x^2) equation:


Simplifying
log(7)(2x2 + -16x) = log(7)(-60 + x2)

Reorder the terms:
glo * 7(-16x + 2x2) = log(7)(-60 + x2)

Reorder the terms for easier multiplication:
7glo(-16x + 2x2) = log(7)(-60 + x2)
(-16x * 7glo + 2x2 * 7glo) = log(7)(-60 + x2)
(-112glox + 14glox2) = log(7)(-60 + x2)

Reorder the terms for easier multiplication:
-112glox + 14glox2 = 7glo(-60 + x2)
-112glox + 14glox2 = (-60 * 7glo + x2 * 7glo)
-112glox + 14glox2 = (-420glo + 7glox2)

Solving
-112glox + 14glox2 = -420glo + 7glox2

Solving for variable 'g'.

Move all terms containing g to the left, all other terms to the right.

Add '420glo' to each side of the equation.
-112glox + 420glo + 14glox2 = -420glo + 420glo + 7glox2

Reorder the terms:
420glo + -112glox + 14glox2 = -420glo + 420glo + 7glox2

Combine like terms: -420glo + 420glo = 0
420glo + -112glox + 14glox2 = 0 + 7glox2
420glo + -112glox + 14glox2 = 7glox2

Add '-7glox2' to each side of the equation.
420glo + -112glox + 14glox2 + -7glox2 = 7glox2 + -7glox2

Combine like terms: 14glox2 + -7glox2 = 7glox2
420glo + -112glox + 7glox2 = 7glox2 + -7glox2

Combine like terms: 7glox2 + -7glox2 = 0
420glo + -112glox + 7glox2 = 0

Factor out the Greatest Common Factor (GCF), '7glo'.
7glo(60 + -16x + x2) = 0

Factor a trinomial.
7glo((6 + -1x)(10 + -1x)) = 0

Ignore the factor 7.

Subproblem 1

Set the factor 'glo' equal to zero and attempt to solve: Simplifying glo = 0 Solving glo = 0 Move all terms containing g to the left, all other terms to the right. Simplifying glo = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Add 'x' to each side of the equation. -1x + x = -6 + x Combine like terms: -1x + x = 0 0 = -6 + x Simplifying 0 = -6 + x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 3

Set the factor '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Add 'x' to each side of the equation. -1x + x = -10 + x Combine like terms: -1x + x = 0 0 = -10 + x Simplifying 0 = -10 + x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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