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Simplifying (4x + 3)(x + -6) = 12x + 9 Reorder the terms: (3 + 4x)(x + -6) = 12x + 9 Reorder the terms: (3 + 4x)(-6 + x) = 12x + 9 Multiply (3 + 4x) * (-6 + x) (3(-6 + x) + 4x * (-6 + x)) = 12x + 9 ((-6 * 3 + x * 3) + 4x * (-6 + x)) = 12x + 9 ((-18 + 3x) + 4x * (-6 + x)) = 12x + 9 (-18 + 3x + (-6 * 4x + x * 4x)) = 12x + 9 (-18 + 3x + (-24x + 4x2)) = 12x + 9 Combine like terms: 3x + -24x = -21x (-18 + -21x + 4x2) = 12x + 9 Reorder the terms: -18 + -21x + 4x2 = 9 + 12x Solving -18 + -21x + 4x2 = 9 + 12x Solving for variable 'x'. Reorder the terms: -18 + -9 + -21x + -12x + 4x2 = 9 + 12x + -9 + -12x Combine like terms: -18 + -9 = -27 -27 + -21x + -12x + 4x2 = 9 + 12x + -9 + -12x Combine like terms: -21x + -12x = -33x -27 + -33x + 4x2 = 9 + 12x + -9 + -12x Reorder the terms: -27 + -33x + 4x2 = 9 + -9 + 12x + -12x Combine like terms: 9 + -9 = 0 -27 + -33x + 4x2 = 0 + 12x + -12x -27 + -33x + 4x2 = 12x + -12x Combine like terms: 12x + -12x = 0 -27 + -33x + 4x2 = 0 Factor a trinomial. (-3 + -4x)(9 + -1x) = 0Subproblem 1
Set the factor '(-3 + -4x)' equal to zero and attempt to solve: Simplifying -3 + -4x = 0 Solving -3 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -4x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4x = 0 + 3 -4x = 0 + 3 Combine like terms: 0 + 3 = 3 -4x = 3 Divide each side by '-4'. x = -0.75 Simplifying x = -0.75Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9Solution
x = {-0.75, 9}
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