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Simplifying 2x(7x + -6)(x + 6) = 0 Reorder the terms: 2x(-6 + 7x)(x + 6) = 0 Reorder the terms: 2x(-6 + 7x)(6 + x) = 0 Multiply (-6 + 7x) * (6 + x) 2x(-6(6 + x) + 7x * (6 + x)) = 0 2x((6 * -6 + x * -6) + 7x * (6 + x)) = 0 2x((-36 + -6x) + 7x * (6 + x)) = 0 2x(-36 + -6x + (6 * 7x + x * 7x)) = 0 2x(-36 + -6x + (42x + 7x2)) = 0 Combine like terms: -6x + 42x = 36x 2x(-36 + 36x + 7x2) = 0 (-36 * 2x + 36x * 2x + 7x2 * 2x) = 0 (-72x + 72x2 + 14x3) = 0 Solving -72x + 72x2 + 14x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-36 + 36x + 7x2) = 0 Factor a trinomial. 2x((-6 + -1x)(6 + -7x)) = 0 Ignore the factor 2.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 '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 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 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Divide each side by '-1'. x = -6 Simplifying x = -6Subproblem 3
Set the factor '(6 + -7x)' equal to zero and attempt to solve: Simplifying 6 + -7x = 0 Solving 6 + -7x = 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 + -7x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -7x = 0 + -6 -7x = 0 + -6 Combine like terms: 0 + -6 = -6 -7x = -6 Divide each side by '-7'. x = 0.8571428571 Simplifying x = 0.8571428571Solution
x = {0, -6, 0.8571428571}
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