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

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

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

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

Reorder the terms:
5(-7 + g) * 2[g + -3(-5 + g)] = 0
5(-7 + g) * 2[g + (-5 * -3 + g * -3)] = 0
5(-7 + g) * 2[g + (15 + -3g)] = 0

Reorder the terms:
5(-7 + g) * 2[15 + g + -3g] = 0

Combine like terms: g + -3g = -2g
5(-7 + g) * 2[15 + -2g] = 0

Reorder the terms for easier multiplication:
5 * 2(-7 + g)[15 + -2g] = 0

Multiply 5 * 2
10(-7 + g)[15 + -2g] = 0

Multiply (-7 + g) * [15 + -2g]
10(-7[15 + -2g] + g[15 + -2g]) = 0
10([15 * -7 + -2g * -7] + g[15 + -2g]) = 0
10([-105 + 14g] + g[15 + -2g]) = 0
10(-105 + 14g + [15 * g + -2g * g]) = 0
10(-105 + 14g + [15g + -2g2]) = 0

Combine like terms: 14g + 15g = 29g
10(-105 + 29g + -2g2) = 0
(-105 * 10 + 29g * 10 + -2g2 * 10) = 0
(-1050 + 290g + -20g2) = 0

Solving
-1050 + 290g + -20g2 = 0

Solving for variable 'g'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-105 + 29g + -2g2) = 0

Factor a trinomial.
10((-15 + 2g)(7 + -1g)) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(-15 + 2g)' equal to zero and attempt to solve:

Simplifying
-15 + 2g = 0

Solving
-15 + 2g = 0

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

Add '15' to each side of the equation.
-15 + 15 + 2g = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 2g = 0 + 15
2g = 0 + 15

Combine like terms: 0 + 15 = 15
2g = 15

Divide each side by '2'.
g = 7.5

Simplifying
g = 7.5
Subproblem 2
Set the factor '(7 + -1g)' equal to zero and attempt to solve:

Simplifying
7 + -1g = 0

Solving
7 + -1g = 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 + -1g = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1g = 0 + -7
-1g = 0 + -7

Combine like terms: 0 + -7 = -7
-1g = -7

Divide each side by '-1'.
g = 7

Simplifying
g = 7
Solution
g = {7.5, 7}