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