5(g-7)+2[g-3g(g-5)]=0

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Solution for 5(g-7)+2[g-3g(g-5)]=0 equation: 


Simplifying
5(g + -7) + 2[g + -3g(g + -5)] = 0

Reorder the terms:
5(-7 + g) + 2[g + -3g(g + -5)] = 0
(-7 * 5 + g * 5) + 2[g + -3g(g + -5)] = 0
(-35 + 5g) + 2[g + -3g(g + -5)] = 0

Reorder the terms:
-35 + 5g + 2[g + -3g(-5 + g)] = 0
-35 + 5g + 2[g + (-5 * -3g + g * -3g)] = 0
-35 + 5g + 2[g + (15g + -3g2)] = 0

Combine like terms: g + 15g = 16g
-35 + 5g + 2[16g + -3g2] = 0
-35 + 5g + [16g * 2 + -3g2 * 2] = 0
-35 + 5g + [32g + -6g2] = 0

Combine like terms: 5g + 32g = 37g
-35 + 37g + -6g2 = 0

Solving
-35 + 37g + -6g2 = 0

Solving for variable 'g'.

Factor a trinomial.
(-5 + g)(7 + -6g) = 0


Subproblem 1
Set the factor '(-5 + g)' equal to zero and attempt to solve:

Simplifying
-5 + g = 0

Solving
-5 + g = 0

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

Add '5' to each side of the equation.
-5 + 5 + g = 0 + 5

Combine like terms: -5 + 5 = 0
0 + g = 0 + 5
g = 0 + 5

Combine like terms: 0 + 5 = 5
g = 5

Simplifying
g = 5

Subproblem 2
Set the factor '(7 + -6g)' equal to zero and attempt to solve:

Simplifying
7 + -6g = 0

Solving
7 + -6g = 0

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

Add '-7' to each side of the equation.
7 + -7 + -6g = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -6g = 0 + -7
-6g = 0 + -7

Combine like terms: 0 + -7 = -7
-6g = -7

Divide each side by '-6'.
g = 1.166666667

Simplifying
g = 1.166666667
Solution
g = {5, 1.166666667}

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