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Simplifying 0 = 4(4x + -3)(x + -5) Reorder the terms: 0 = 4(-3 + 4x)(x + -5) Reorder the terms: 0 = 4(-3 + 4x)(-5 + x) Multiply (-3 + 4x) * (-5 + x) 0 = 4(-3(-5 + x) + 4x * (-5 + x)) 0 = 4((-5 * -3 + x * -3) + 4x * (-5 + x)) 0 = 4((15 + -3x) + 4x * (-5 + x)) 0 = 4(15 + -3x + (-5 * 4x + x * 4x)) 0 = 4(15 + -3x + (-20x + 4x2)) Combine like terms: -3x + -20x = -23x 0 = 4(15 + -23x + 4x2) 0 = (15 * 4 + -23x * 4 + 4x2 * 4) 0 = (60 + -92x + 16x2) Solving 0 = 60 + -92x + 16x2 Solving for variable 'x'. Combine like terms: 0 + -60 = -60 -60 + 92x + -16x2 = 60 + -92x + 16x2 + -60 + 92x + -16x2 Reorder the terms: -60 + 92x + -16x2 = 60 + -60 + -92x + 92x + 16x2 + -16x2 Combine like terms: 60 + -60 = 0 -60 + 92x + -16x2 = 0 + -92x + 92x + 16x2 + -16x2 -60 + 92x + -16x2 = -92x + 92x + 16x2 + -16x2 Combine like terms: -92x + 92x = 0 -60 + 92x + -16x2 = 0 + 16x2 + -16x2 -60 + 92x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 -60 + 92x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-15 + 23x + -4x2) = 0 Factor a trinomial. 4((-5 + x)(3 + -4x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve: Simplifying -5 + x = 0 Solving -5 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0 + 5 x = 0 + 5 Combine like terms: 0 + 5 = 5 x = 5 Simplifying x = 5Subproblem 2
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 = 0.75Solution
x = {5, 0.75}
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