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Simplifying (x + 4)(6x + -3) = 0 Reorder the terms: (4 + x)(6x + -3) = 0 Reorder the terms: (4 + x)(-3 + 6x) = 0 Multiply (4 + x) * (-3 + 6x) (4(-3 + 6x) + x(-3 + 6x)) = 0 ((-3 * 4 + 6x * 4) + x(-3 + 6x)) = 0 ((-12 + 24x) + x(-3 + 6x)) = 0 (-12 + 24x + (-3 * x + 6x * x)) = 0 (-12 + 24x + (-3x + 6x2)) = 0 Combine like terms: 24x + -3x = 21x (-12 + 21x + 6x2) = 0 Solving -12 + 21x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-4 + 7x + 2x2) = 0 Factor a trinomial. 3((-4 + -1x)(1 + -2x)) = 0 Ignore the factor 3.Subproblem 1
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 2
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 = {-4, 0.5}
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