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Simplifying x(4x + -7)(x + 6) = 0 Reorder the terms: x(-7 + 4x)(x + 6) = 0 Reorder the terms: x(-7 + 4x)(6 + x) = 0 Multiply (-7 + 4x) * (6 + x) x(-7(6 + x) + 4x * (6 + x)) = 0 x((6 * -7 + x * -7) + 4x * (6 + x)) = 0 x((-42 + -7x) + 4x * (6 + x)) = 0 x(-42 + -7x + (6 * 4x + x * 4x)) = 0 x(-42 + -7x + (24x + 4x2)) = 0 Combine like terms: -7x + 24x = 17x x(-42 + 17x + 4x2) = 0 (-42 * x + 17x * x + 4x2 * x) = 0 (-42x + 17x2 + 4x3) = 0 Solving -42x + 17x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-42 + 17x + 4x2) = 0 Factor a trinomial. x((-6 + -1x)(7 + -4x)) = 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 + -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 '(7 + -4x)' equal to zero and attempt to solve: Simplifying 7 + -4x = 0 Solving 7 + -4x = 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 + -4x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4x = 0 + -7 -4x = 0 + -7 Combine like terms: 0 + -7 = -7 -4x = -7 Divide each side by '-4'. x = 1.75 Simplifying x = 1.75Solution
x = {0, -6, 1.75}
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