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Simplifying (4x + 10)(8x + -3) = 0 Reorder the terms: (10 + 4x)(8x + -3) = 0 Reorder the terms: (10 + 4x)(-3 + 8x) = 0 Multiply (10 + 4x) * (-3 + 8x) (10(-3 + 8x) + 4x * (-3 + 8x)) = 0 ((-3 * 10 + 8x * 10) + 4x * (-3 + 8x)) = 0 ((-30 + 80x) + 4x * (-3 + 8x)) = 0 (-30 + 80x + (-3 * 4x + 8x * 4x)) = 0 (-30 + 80x + (-12x + 32x2)) = 0 Combine like terms: 80x + -12x = 68x (-30 + 68x + 32x2) = 0 Solving -30 + 68x + 32x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-15 + 34x + 16x2) = 0 Factor a trinomial. 2((-5 + -2x)(3 + -8x)) = 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 '(3 + -8x)' equal to zero and attempt to solve: Simplifying 3 + -8x = 0 Solving 3 + -8x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -8x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -8x = 0 + -3 -8x = 0 + -3 Combine like terms: 0 + -3 = -3 -8x = -3 Divide each side by '-8'. x = 0.375 Simplifying x = 0.375Solution
x = {-2.5, 0.375}
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