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Simplifying f(0) = 4x(x + -11)(x + 7) Reorder the terms for easier multiplication: 0f = 4x(x + -11)(x + 7) Anything times zero is zero. 0f = 4x(x + -11)(x + 7) Reorder the terms: 0 = 4x(-11 + x)(x + 7) Reorder the terms: 0 = 4x(-11 + x)(7 + x) Multiply (-11 + x) * (7 + x) 0 = 4x(-11(7 + x) + x(7 + x)) 0 = 4x((7 * -11 + x * -11) + x(7 + x)) 0 = 4x((-77 + -11x) + x(7 + x)) 0 = 4x(-77 + -11x + (7 * x + x * x)) 0 = 4x(-77 + -11x + (7x + x2)) Combine like terms: -11x + 7x = -4x 0 = 4x(-77 + -4x + x2) 0 = (-77 * 4x + -4x * 4x + x2 * 4x) 0 = (-308x + -16x2 + 4x3) Solving 0 = -308x + -16x2 + 4x3 Solving for variable 'x'. Remove the zero: 308x + 16x2 + -4x3 = -308x + -16x2 + 4x3 + 308x + 16x2 + -4x3 Reorder the terms: 308x + 16x2 + -4x3 = -308x + 308x + -16x2 + 16x2 + 4x3 + -4x3 Combine like terms: -308x + 308x = 0 308x + 16x2 + -4x3 = 0 + -16x2 + 16x2 + 4x3 + -4x3 308x + 16x2 + -4x3 = -16x2 + 16x2 + 4x3 + -4x3 Combine like terms: -16x2 + 16x2 = 0 308x + 16x2 + -4x3 = 0 + 4x3 + -4x3 308x + 16x2 + -4x3 = 4x3 + -4x3 Combine like terms: 4x3 + -4x3 = 0 308x + 16x2 + -4x3 = 0 Factor out the Greatest Common Factor (GCF), '4x'. 4x(77 + 4x + -1x2) = 0 Factor a trinomial. 4x((11 + -1x)(7 + x)) = 0 Ignore the factor 4.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 '(11 + -1x)' equal to zero and attempt to solve: Simplifying 11 + -1x = 0 Solving 11 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -1x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -1x = 0 + -11 -1x = 0 + -11 Combine like terms: 0 + -11 = -11 -1x = -11 Divide each side by '-1'. x = 11 Simplifying x = 11Subproblem 3
Set the factor '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 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 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7Solution
x = {0, 11, -7}
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