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Simplifying 2(3x + -4)(2x + 5) = 0 Reorder the terms: 2(-4 + 3x)(2x + 5) = 0 Reorder the terms: 2(-4 + 3x)(5 + 2x) = 0 Multiply (-4 + 3x) * (5 + 2x) 2(-4(5 + 2x) + 3x * (5 + 2x)) = 0 2((5 * -4 + 2x * -4) + 3x * (5 + 2x)) = 0 2((-20 + -8x) + 3x * (5 + 2x)) = 0 2(-20 + -8x + (5 * 3x + 2x * 3x)) = 0 2(-20 + -8x + (15x + 6x2)) = 0 Combine like terms: -8x + 15x = 7x 2(-20 + 7x + 6x2) = 0 (-20 * 2 + 7x * 2 + 6x2 * 2) = 0 (-40 + 14x + 12x2) = 0 Solving -40 + 14x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-20 + 7x + 6x2) = 0 Factor a trinomial. 2((-5 + -2x)(4 + -3x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -2x)' equal to zero and attempt to solve: Simplifying -5 + -2x = 0 Solving -5 + -2x = 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 + -2x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2x = 0 + 5 -2x = 0 + 5 Combine like terms: 0 + 5 = 5 -2x = 5 Divide each side by '-2'. x = -2.5 Simplifying x = -2.5Subproblem 2
Set the factor '(4 + -3x)' equal to zero and attempt to solve: Simplifying 4 + -3x = 0 Solving 4 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3x = 0 + -4 -3x = 0 + -4 Combine like terms: 0 + -4 = -4 -3x = -4 Divide each side by '-3'. x = 1.333333333 Simplifying x = 1.333333333Solution
x = {-2.5, 1.333333333}
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