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Simplifying 2x(x + 4)(6x + -3) = 0 Reorder the terms: 2x(4 + x)(6x + -3) = 0 Reorder the terms: 2x(4 + x)(-3 + 6x) = 0 Multiply (4 + x) * (-3 + 6x) 2x(4(-3 + 6x) + x(-3 + 6x)) = 0 2x((-3 * 4 + 6x * 4) + x(-3 + 6x)) = 0 2x((-12 + 24x) + x(-3 + 6x)) = 0 2x(-12 + 24x + (-3 * x + 6x * x)) = 0 2x(-12 + 24x + (-3x + 6x2)) = 0 Combine like terms: 24x + -3x = 21x 2x(-12 + 21x + 6x2) = 0 (-12 * 2x + 21x * 2x + 6x2 * 2x) = 0 (-24x + 42x2 + 12x3) = 0 Solving -24x + 42x2 + 12x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6x'. 6x(-4 + 7x + 2x2) = 0 Factor a trinomial. 6x((-4 + -1x)(1 + -2x)) = 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 '(-4 + -1x)' equal to zero and attempt to solve: Simplifying -4 + -1x = 0 Solving -4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x = 0 + 4 -1x = 0 + 4 Combine like terms: 0 + 4 = 4 -1x = 4 Divide each side by '-1'. x = -4 Simplifying x = -4Subproblem 3
Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5Solution
x = {0, -4, 0.5}
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