3g(g)-2g(g-7)=g(g+6)-28

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Solution for 3g(g)-2g(g-7)=g(g+6)-28 equation: 


Simplifying
3g(g) + -2g(g + -7) = g(g + 6) + -28

Multiply g * g
3g2 + -2g(g + -7) = g(g + 6) + -28

Reorder the terms:
3g2 + -2g(-7 + g) = g(g + 6) + -28
3g2 + (-7 * -2g + g * -2g) = g(g + 6) + -28
3g2 + (14g + -2g2) = g(g + 6) + -28

Reorder the terms:
14g + 3g2 + -2g2 = g(g + 6) + -28

Combine like terms: 3g2 + -2g2 = 1g2
14g + 1g2 = g(g + 6) + -28

Reorder the terms:
14g + 1g2 = g(6 + g) + -28
14g + 1g2 = (6 * g + g * g) + -28
14g + 1g2 = (6g + g2) + -28

Reorder the terms:
14g + 1g2 = -28 + 6g + g2

Solving
14g + 1g2 = -28 + 6g + g2

Solving for variable 'g'.

Reorder the terms:
28 + 14g + -6g + 1g2 + -1g2 = -28 + 6g + g2 + 28 + -6g + -1g2

Combine like terms: 14g + -6g = 8g
28 + 8g + 1g2 + -1g2 = -28 + 6g + g2 + 28 + -6g + -1g2

Combine like terms: 1g2 + -1g2 = 0
28 + 8g + 0 = -28 + 6g + g2 + 28 + -6g + -1g2
28 + 8g = -28 + 6g + g2 + 28 + -6g + -1g2

Reorder the terms:
28 + 8g = -28 + 28 + 6g + -6g + g2 + -1g2

Combine like terms: -28 + 28 = 0
28 + 8g = 0 + 6g + -6g + g2 + -1g2
28 + 8g = 6g + -6g + g2 + -1g2

Combine like terms: 6g + -6g = 0
28 + 8g = 0 + g2 + -1g2
28 + 8g = g2 + -1g2

Combine like terms: g2 + -1g2 = 0
28 + 8g = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(7 + 2g) = 0

Ignore the factor 4.

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

Simplifying
7 + 2g = 0

Solving
7 + 2g = 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 + 2g = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2g = 0 + -7
2g = 0 + -7

Combine like terms: 0 + -7 = -7
2g = -7

Divide each side by '2'.
g = -3.5

Simplifying
g = -3.5
Solution
g = {-3.5}

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