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Simplifying x(x + -5)(3x + 7) = 0 Reorder the terms: x(-5 + x)(3x + 7) = 0 Reorder the terms: x(-5 + x)(7 + 3x) = 0 Multiply (-5 + x) * (7 + 3x) x(-5(7 + 3x) + x(7 + 3x)) = 0 x((7 * -5 + 3x * -5) + x(7 + 3x)) = 0 x((-35 + -15x) + x(7 + 3x)) = 0 x(-35 + -15x + (7 * x + 3x * x)) = 0 x(-35 + -15x + (7x + 3x2)) = 0 Combine like terms: -15x + 7x = -8x x(-35 + -8x + 3x2) = 0 (-35 * x + -8x * x + 3x2 * x) = 0 (-35x + -8x2 + 3x3) = 0 Solving -35x + -8x2 + 3x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-35 + -8x + 3x2) = 0 Factor a trinomial. x((-7 + -3x)(5 + -1x)) = 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 + -3x)' equal to zero and attempt to solve: Simplifying -7 + -3x = 0 Solving -7 + -3x = 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 + -3x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -3x = 0 + 7 -3x = 0 + 7 Combine like terms: 0 + 7 = 7 -3x = 7 Divide each side by '-3'. x = -2.333333333 Simplifying x = -2.333333333Subproblem 3
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {0, -2.333333333, 5}
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