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Simplifying 6x(7x + -9)(x + 6) = 0 Reorder the terms: 6x(-9 + 7x)(x + 6) = 0 Reorder the terms: 6x(-9 + 7x)(6 + x) = 0 Multiply (-9 + 7x) * (6 + x) 6x(-9(6 + x) + 7x * (6 + x)) = 0 6x((6 * -9 + x * -9) + 7x * (6 + x)) = 0 6x((-54 + -9x) + 7x * (6 + x)) = 0 6x(-54 + -9x + (6 * 7x + x * 7x)) = 0 6x(-54 + -9x + (42x + 7x2)) = 0 Combine like terms: -9x + 42x = 33x 6x(-54 + 33x + 7x2) = 0 (-54 * 6x + 33x * 6x + 7x2 * 6x) = 0 (-324x + 198x2 + 42x3) = 0 Solving -324x + 198x2 + 42x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6x'. 6x(-54 + 33x + 7x2) = 0 Factor a trinomial. 6x((-6 + -1x)(9 + -7x)) = 0 Ignore the factor 6.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 '(9 + -7x)' equal to zero and attempt to solve: Simplifying 9 + -7x = 0 Solving 9 + -7x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -7x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -7x = 0 + -9 -7x = 0 + -9 Combine like terms: 0 + -9 = -9 -7x = -9 Divide each side by '-7'. x = 1.285714286 Simplifying x = 1.285714286Solution
x = {0, -6, 1.285714286}
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