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Simplifying (5x + 4)(6x + -4) = 0 Reorder the terms: (4 + 5x)(6x + -4) = 0 Reorder the terms: (4 + 5x)(-4 + 6x) = 0 Multiply (4 + 5x) * (-4 + 6x) (4(-4 + 6x) + 5x * (-4 + 6x)) = 0 ((-4 * 4 + 6x * 4) + 5x * (-4 + 6x)) = 0 ((-16 + 24x) + 5x * (-4 + 6x)) = 0 (-16 + 24x + (-4 * 5x + 6x * 5x)) = 0 (-16 + 24x + (-20x + 30x2)) = 0 Combine like terms: 24x + -20x = 4x (-16 + 4x + 30x2) = 0 Solving -16 + 4x + 30x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + 2x + 15x2) = 0 Factor a trinomial. 2((-4 + -5x)(2 + -3x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + -5x)' equal to zero and attempt to solve: Simplifying -4 + -5x = 0 Solving -4 + -5x = 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 + -5x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -5x = 0 + 4 -5x = 0 + 4 Combine like terms: 0 + 4 = 4 -5x = 4 Divide each side by '-5'. x = -0.8 Simplifying x = -0.8Subproblem 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 = {-0.8, 0.6666666667}
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