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Simplifying 18(x + -6) = 6(2x + 3) + 4(2x + 3)(x + -6) Reorder the terms: 18(-6 + x) = 6(2x + 3) + 4(2x + 3)(x + -6) (-6 * 18 + x * 18) = 6(2x + 3) + 4(2x + 3)(x + -6) (-108 + 18x) = 6(2x + 3) + 4(2x + 3)(x + -6) Reorder the terms: -108 + 18x = 6(3 + 2x) + 4(2x + 3)(x + -6) -108 + 18x = (3 * 6 + 2x * 6) + 4(2x + 3)(x + -6) -108 + 18x = (18 + 12x) + 4(2x + 3)(x + -6) Reorder the terms: -108 + 18x = 18 + 12x + 4(3 + 2x)(x + -6) Reorder the terms: -108 + 18x = 18 + 12x + 4(3 + 2x)(-6 + x) Multiply (3 + 2x) * (-6 + x) -108 + 18x = 18 + 12x + 4(3(-6 + x) + 2x * (-6 + x)) -108 + 18x = 18 + 12x + 4((-6 * 3 + x * 3) + 2x * (-6 + x)) -108 + 18x = 18 + 12x + 4((-18 + 3x) + 2x * (-6 + x)) -108 + 18x = 18 + 12x + 4(-18 + 3x + (-6 * 2x + x * 2x)) -108 + 18x = 18 + 12x + 4(-18 + 3x + (-12x + 2x2)) Combine like terms: 3x + -12x = -9x -108 + 18x = 18 + 12x + 4(-18 + -9x + 2x2) -108 + 18x = 18 + 12x + (-18 * 4 + -9x * 4 + 2x2 * 4) -108 + 18x = 18 + 12x + (-72 + -36x + 8x2) Reorder the terms: -108 + 18x = 18 + -72 + 12x + -36x + 8x2 Combine like terms: 18 + -72 = -54 -108 + 18x = -54 + 12x + -36x + 8x2 Combine like terms: 12x + -36x = -24x -108 + 18x = -54 + -24x + 8x2 Solving -108 + 18x = -54 + -24x + 8x2 Solving for variable 'x'. Reorder the terms: -108 + 54 + 18x + 24x + -8x2 = -54 + -24x + 8x2 + 54 + 24x + -8x2 Combine like terms: -108 + 54 = -54 -54 + 18x + 24x + -8x2 = -54 + -24x + 8x2 + 54 + 24x + -8x2 Combine like terms: 18x + 24x = 42x -54 + 42x + -8x2 = -54 + -24x + 8x2 + 54 + 24x + -8x2 Reorder the terms: -54 + 42x + -8x2 = -54 + 54 + -24x + 24x + 8x2 + -8x2 Combine like terms: -54 + 54 = 0 -54 + 42x + -8x2 = 0 + -24x + 24x + 8x2 + -8x2 -54 + 42x + -8x2 = -24x + 24x + 8x2 + -8x2 Combine like terms: -24x + 24x = 0 -54 + 42x + -8x2 = 0 + 8x2 + -8x2 -54 + 42x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 -54 + 42x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-27 + 21x + -4x2) = 0 Factor a trinomial. 2((-3 + x)(9 + -4x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 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 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Simplifying x = 3Subproblem 2
Set the factor '(9 + -4x)' equal to zero and attempt to solve: Simplifying 9 + -4x = 0 Solving 9 + -4x = 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 + -4x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -4x = 0 + -9 -4x = 0 + -9 Combine like terms: 0 + -9 = -9 -4x = -9 Divide each side by '-4'. x = 2.25 Simplifying x = 2.25Solution
x = {3, 2.25}
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