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Simplifying 5k2 + -7k + 12 = 4(-2k + 3) Reorder the terms: 12 + -7k + 5k2 = 4(-2k + 3) Reorder the terms: 12 + -7k + 5k2 = 4(3 + -2k) 12 + -7k + 5k2 = (3 * 4 + -2k * 4) 12 + -7k + 5k2 = (12 + -8k) Add '-12' to each side of the equation. 12 + -7k + -12 + 5k2 = 12 + -12 + -8k Reorder the terms: 12 + -12 + -7k + 5k2 = 12 + -12 + -8k Combine like terms: 12 + -12 = 0 0 + -7k + 5k2 = 12 + -12 + -8k -7k + 5k2 = 12 + -12 + -8k Combine like terms: 12 + -12 = 0 -7k + 5k2 = 0 + -8k -7k + 5k2 = -8k Solving -7k + 5k2 = -8k Solving for variable 'k'. Reorder the terms: -7k + 8k + 5k2 = -8k + 8k Combine like terms: -7k + 8k = 1k 1k + 5k2 = -8k + 8k Combine like terms: -8k + 8k = 0 1k + 5k2 = 0 Factor out the Greatest Common Factor (GCF), 'k'. k(1 + 5k) = 0Subproblem 1
Set the factor 'k' equal to zero and attempt to solve: Simplifying k = 0 Solving k = 0 Move all terms containing k to the left, all other terms to the right. Simplifying k = 0Subproblem 2
Set the factor '(1 + 5k)' equal to zero and attempt to solve: Simplifying 1 + 5k = 0 Solving 1 + 5k = 0 Move all terms containing k to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 5k = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 5k = 0 + -1 5k = 0 + -1 Combine like terms: 0 + -1 = -1 5k = -1 Divide each side by '5'. k = -0.2 Simplifying k = -0.2Solution
k = {0, -0.2}
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