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Simplifying 0 = (4 + -8x)(5 + 6x) Multiply (4 + -8x) * (5 + 6x) 0 = (4(5 + 6x) + -8x * (5 + 6x)) 0 = ((5 * 4 + 6x * 4) + -8x * (5 + 6x)) 0 = ((20 + 24x) + -8x * (5 + 6x)) 0 = (20 + 24x + (5 * -8x + 6x * -8x)) 0 = (20 + 24x + (-40x + -48x2)) Combine like terms: 24x + -40x = -16x 0 = (20 + -16x + -48x2) Solving 0 = 20 + -16x + -48x2 Solving for variable 'x'. Combine like terms: 0 + -20 = -20 -20 + 16x + 48x2 = 20 + -16x + -48x2 + -20 + 16x + 48x2 Reorder the terms: -20 + 16x + 48x2 = 20 + -20 + -16x + 16x + -48x2 + 48x2 Combine like terms: 20 + -20 = 0 -20 + 16x + 48x2 = 0 + -16x + 16x + -48x2 + 48x2 -20 + 16x + 48x2 = -16x + 16x + -48x2 + 48x2 Combine like terms: -16x + 16x = 0 -20 + 16x + 48x2 = 0 + -48x2 + 48x2 -20 + 16x + 48x2 = -48x2 + 48x2 Combine like terms: -48x2 + 48x2 = 0 -20 + 16x + 48x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-5 + 4x + 12x2) = 0 Factor a trinomial. 4((-5 + -6x)(1 + -2x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-5 + -6x)' equal to zero and attempt to solve: Simplifying -5 + -6x = 0 Solving -5 + -6x = 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 + -6x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -6x = 0 + 5 -6x = 0 + 5 Combine like terms: 0 + 5 = 5 -6x = 5 Divide each side by '-6'. x = -0.8333333333 Simplifying x = -0.8333333333Subproblem 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 = {-0.8333333333, 0.5}
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