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Simplifying (2x + 6) * x(-7x + 14) = 0 Reorder the terms: (6 + 2x) * x(-7x + 14) = 0 Reorder the terms: (6 + 2x) * x(14 + -7x) = 0 Reorder the terms for easier multiplication: x(6 + 2x)(14 + -7x) = 0 Multiply (6 + 2x) * (14 + -7x) x(6(14 + -7x) + 2x * (14 + -7x)) = 0 x((14 * 6 + -7x * 6) + 2x * (14 + -7x)) = 0 x((84 + -42x) + 2x * (14 + -7x)) = 0 x(84 + -42x + (14 * 2x + -7x * 2x)) = 0 x(84 + -42x + (28x + -14x2)) = 0 Combine like terms: -42x + 28x = -14x x(84 + -14x + -14x2) = 0 (84 * x + -14x * x + -14x2 * x) = 0 (84x + -14x2 + -14x3) = 0 Solving 84x + -14x2 + -14x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '14x'. 14x(6 + -1x + -1x2) = 0 Factor a trinomial. 14x((2 + -1x)(3 + x)) = 0 Ignore the factor 14.Subproblem 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 '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Subproblem 3
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Solution
x = {0, 2, -3}
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