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Simplifying 16(x + -7)(2x + 3) = 0 Reorder the terms: 16(-7 + x)(2x + 3) = 0 Reorder the terms: 16(-7 + x)(3 + 2x) = 0 Multiply (-7 + x) * (3 + 2x) 16(-7(3 + 2x) + x(3 + 2x)) = 0 16((3 * -7 + 2x * -7) + x(3 + 2x)) = 0 16((-21 + -14x) + x(3 + 2x)) = 0 16(-21 + -14x + (3 * x + 2x * x)) = 0 16(-21 + -14x + (3x + 2x2)) = 0 Combine like terms: -14x + 3x = -11x 16(-21 + -11x + 2x2) = 0 (-21 * 16 + -11x * 16 + 2x2 * 16) = 0 (-336 + -176x + 32x2) = 0 Solving -336 + -176x + 32x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '16'. 16(-21 + -11x + 2x2) = 0 Factor a trinomial. 16((-3 + -2x)(7 + -1x)) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve: Simplifying -3 + -2x = 0 Solving -3 + -2x = 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 + -2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2x = 0 + 3 -2x = 0 + 3 Combine like terms: 0 + 3 = 3 -2x = 3 Divide each side by '-2'. x = -1.5 Simplifying x = -1.5Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Solution
x = {-1.5, 7}
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