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Simplifying 4(6x2 + 13x + 5) = 0 Reorder the terms: 4(5 + 13x + 6x2) = 0 (5 * 4 + 13x * 4 + 6x2 * 4) = 0 (20 + 52x + 24x2) = 0 Solving 20 + 52x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(5 + 13x + 6x2) = 0 Factor a trinomial. 4((5 + 3x)(1 + 2x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(5 + 3x)' equal to zero and attempt to solve: Simplifying 5 + 3x = 0 Solving 5 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 3x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3x = 0 + -5 3x = 0 + -5 Combine like terms: 0 + -5 = -5 3x = -5 Divide each side by '3'. x = -1.666666667 Simplifying x = -1.666666667Subproblem 2
Set the factor '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Divide each side by '2'. x = -0.5 Simplifying x = -0.5Solution
x = {-1.666666667, -0.5}
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