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Simplifying 0 = (6x + 4)(10x + 20) Reorder the terms: 0 = (4 + 6x)(10x + 20) Reorder the terms: 0 = (4 + 6x)(20 + 10x) Multiply (4 + 6x) * (20 + 10x) 0 = (4(20 + 10x) + 6x * (20 + 10x)) 0 = ((20 * 4 + 10x * 4) + 6x * (20 + 10x)) 0 = ((80 + 40x) + 6x * (20 + 10x)) 0 = (80 + 40x + (20 * 6x + 10x * 6x)) 0 = (80 + 40x + (120x + 60x2)) Combine like terms: 40x + 120x = 160x 0 = (80 + 160x + 60x2) Solving 0 = 80 + 160x + 60x2 Solving for variable 'x'. Combine like terms: 0 + -80 = -80 -80 + -160x + -60x2 = 80 + 160x + 60x2 + -80 + -160x + -60x2 Reorder the terms: -80 + -160x + -60x2 = 80 + -80 + 160x + -160x + 60x2 + -60x2 Combine like terms: 80 + -80 = 0 -80 + -160x + -60x2 = 0 + 160x + -160x + 60x2 + -60x2 -80 + -160x + -60x2 = 160x + -160x + 60x2 + -60x2 Combine like terms: 160x + -160x = 0 -80 + -160x + -60x2 = 0 + 60x2 + -60x2 -80 + -160x + -60x2 = 60x2 + -60x2 Combine like terms: 60x2 + -60x2 = 0 -80 + -160x + -60x2 = 0 Factor out the Greatest Common Factor (GCF), '-20'. -20(4 + 8x + 3x2) = 0 Factor a trinomial. -20((2 + x)(2 + 3x)) = 0 Ignore the factor -20.Subproblem 1
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Subproblem 2
Set the factor '(2 + 3x)' equal to zero and attempt to solve: Simplifying 2 + 3x = 0 Solving 2 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3x = 0 + -2 3x = 0 + -2 Combine like terms: 0 + -2 = -2 3x = -2 Divide each side by '3'. x = -0.6666666667 Simplifying x = -0.6666666667Solution
x = {-2, -0.6666666667}
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