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Simplifying (2x + 7) * x(x + 6) = 0 Reorder the terms: (7 + 2x) * x(x + 6) = 0 Reorder the terms: (7 + 2x) * x(6 + x) = 0 Reorder the terms for easier multiplication: x(7 + 2x)(6 + x) = 0 Multiply (7 + 2x) * (6 + x) x(7(6 + x) + 2x * (6 + x)) = 0 x((6 * 7 + x * 7) + 2x * (6 + x)) = 0 x((42 + 7x) + 2x * (6 + x)) = 0 x(42 + 7x + (6 * 2x + x * 2x)) = 0 x(42 + 7x + (12x + 2x2)) = 0 Combine like terms: 7x + 12x = 19x x(42 + 19x + 2x2) = 0 (42 * x + 19x * x + 2x2 * x) = 0 (42x + 19x2 + 2x3) = 0 Solving 42x + 19x2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(42 + 19x + 2x2) = 0 Factor a trinomial. x((6 + x)(7 + 2x)) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6Subproblem 3
Set the factor '(7 + 2x)' equal to zero and attempt to solve: Simplifying 7 + 2x = 0 Solving 7 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 2x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2x = 0 + -7 2x = 0 + -7 Combine like terms: 0 + -7 = -7 2x = -7 Divide each side by '2'. x = -3.5 Simplifying x = -3.5Solution
x = {0, -6, -3.5}
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