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Simplifying 0 = (6x + 4)(10x + 10) Reorder the terms: 0 = (4 + 6x)(10x + 10) Reorder the terms: 0 = (4 + 6x)(10 + 10x) Multiply (4 + 6x) * (10 + 10x) 0 = (4(10 + 10x) + 6x * (10 + 10x)) 0 = ((10 * 4 + 10x * 4) + 6x * (10 + 10x)) 0 = ((40 + 40x) + 6x * (10 + 10x)) 0 = (40 + 40x + (10 * 6x + 10x * 6x)) 0 = (40 + 40x + (60x + 60x2)) Combine like terms: 40x + 60x = 100x 0 = (40 + 100x + 60x2) Solving 0 = 40 + 100x + 60x2 Solving for variable 'x'. Combine like terms: 0 + -40 = -40 -40 + -100x + -60x2 = 40 + 100x + 60x2 + -40 + -100x + -60x2 Reorder the terms: -40 + -100x + -60x2 = 40 + -40 + 100x + -100x + 60x2 + -60x2 Combine like terms: 40 + -40 = 0 -40 + -100x + -60x2 = 0 + 100x + -100x + 60x2 + -60x2 -40 + -100x + -60x2 = 100x + -100x + 60x2 + -60x2 Combine like terms: 100x + -100x = 0 -40 + -100x + -60x2 = 0 + 60x2 + -60x2 -40 + -100x + -60x2 = 60x2 + -60x2 Combine like terms: 60x2 + -60x2 = 0 -40 + -100x + -60x2 = 0 Factor out the Greatest Common Factor (GCF), '-20'. -20(2 + 5x + 3x2) = 0 Factor a trinomial. -20((1 + x)(2 + 3x)) = 0 Ignore the factor -20.Subproblem 1
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Subproblem 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 = {-1, -0.6666666667}
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