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Simplifying 3g(g + -4) + -2g(g + -7) = g(g + 6) + -28 Reorder the terms: 3g(-4 + g) + -2g(g + -7) = g(g + 6) + -28 (-4 * 3g + g * 3g) + -2g(g + -7) = g(g + 6) + -28 (-12g + 3g2) + -2g(g + -7) = g(g + 6) + -28 Reorder the terms: -12g + 3g2 + -2g(-7 + g) = g(g + 6) + -28 -12g + 3g2 + (-7 * -2g + g * -2g) = g(g + 6) + -28 -12g + 3g2 + (14g + -2g2) = g(g + 6) + -28 Reorder the terms: -12g + 14g + 3g2 + -2g2 = g(g + 6) + -28 Combine like terms: -12g + 14g = 2g 2g + 3g2 + -2g2 = g(g + 6) + -28 Combine like terms: 3g2 + -2g2 = 1g2 2g + 1g2 = g(g + 6) + -28 Reorder the terms: 2g + 1g2 = g(6 + g) + -28 2g + 1g2 = (6 * g + g * g) + -28 2g + 1g2 = (6g + g2) + -28 Reorder the terms: 2g + 1g2 = -28 + 6g + g2 Solving 2g + 1g2 = -28 + 6g + g2 Solving for variable 'g'. Reorder the terms: 28 + 2g + -6g + 1g2 + -1g2 = -28 + 6g + g2 + 28 + -6g + -1g2 Combine like terms: 2g + -6g = -4g 28 + -4g + 1g2 + -1g2 = -28 + 6g + g2 + 28 + -6g + -1g2 Combine like terms: 1g2 + -1g2 = 0 28 + -4g + 0 = -28 + 6g + g2 + 28 + -6g + -1g2 28 + -4g = -28 + 6g + g2 + 28 + -6g + -1g2 Reorder the terms: 28 + -4g = -28 + 28 + 6g + -6g + g2 + -1g2 Combine like terms: -28 + 28 = 0 28 + -4g = 0 + 6g + -6g + g2 + -1g2 28 + -4g = 6g + -6g + g2 + -1g2 Combine like terms: 6g + -6g = 0 28 + -4g = 0 + g2 + -1g2 28 + -4g = g2 + -1g2 Combine like terms: g2 + -1g2 = 0 28 + -4g = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(7 + -1g) = 0 Ignore the factor 4.Subproblem 1
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 = 7Solution
g = {7}
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