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Simplifying 2304 = (x + 16)(x + -4)(4) Reorder the terms: 2304 = (16 + x)(x + -4)(4) Reorder the terms: 2304 = (16 + x)(-4 + x)(4) Reorder the terms for easier multiplication: 2304 = 4(16 + x)(-4 + x) Multiply (16 + x) * (-4 + x) 2304 = 4(16(-4 + x) + x(-4 + x)) 2304 = 4((-4 * 16 + x * 16) + x(-4 + x)) 2304 = 4((-64 + 16x) + x(-4 + x)) 2304 = 4(-64 + 16x + (-4 * x + x * x)) 2304 = 4(-64 + 16x + (-4x + x2)) Combine like terms: 16x + -4x = 12x 2304 = 4(-64 + 12x + x2) 2304 = (-64 * 4 + 12x * 4 + x2 * 4) 2304 = (-256 + 48x + 4x2) Solving 2304 = -256 + 48x + 4x2 Solving for variable 'x'. Combine like terms: 2304 + 256 = 2560 2560 + -48x + -4x2 = -256 + 48x + 4x2 + 256 + -48x + -4x2 Reorder the terms: 2560 + -48x + -4x2 = -256 + 256 + 48x + -48x + 4x2 + -4x2 Combine like terms: -256 + 256 = 0 2560 + -48x + -4x2 = 0 + 48x + -48x + 4x2 + -4x2 2560 + -48x + -4x2 = 48x + -48x + 4x2 + -4x2 Combine like terms: 48x + -48x = 0 2560 + -48x + -4x2 = 0 + 4x2 + -4x2 2560 + -48x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 2560 + -48x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(640 + -12x + -1x2) = 0 Factor a trinomial. 4((20 + -1x)(32 + x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(20 + -1x)' equal to zero and attempt to solve: Simplifying 20 + -1x = 0 Solving 20 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + -1x = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -1x = 0 + -20 -1x = 0 + -20 Combine like terms: 0 + -20 = -20 -1x = -20 Divide each side by '-1'. x = 20 Simplifying x = 20Subproblem 2
Set the factor '(32 + x)' equal to zero and attempt to solve: Simplifying 32 + x = 0 Solving 32 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-32' to each side of the equation. 32 + -32 + x = 0 + -32 Combine like terms: 32 + -32 = 0 0 + x = 0 + -32 x = 0 + -32 Combine like terms: 0 + -32 = -32 x = -32 Simplifying x = -32Solution
x = {20, -32}
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