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Simplifying x(4x + 7)(4x + -7) = 0 Reorder the terms: x(7 + 4x)(4x + -7) = 0 Reorder the terms: x(7 + 4x)(-7 + 4x) = 0 Multiply (7 + 4x) * (-7 + 4x) x(7(-7 + 4x) + 4x * (-7 + 4x)) = 0 x((-7 * 7 + 4x * 7) + 4x * (-7 + 4x)) = 0 x((-49 + 28x) + 4x * (-7 + 4x)) = 0 x(-49 + 28x + (-7 * 4x + 4x * 4x)) = 0 x(-49 + 28x + (-28x + 16x2)) = 0 Combine like terms: 28x + -28x = 0 x(-49 + 0 + 16x2) = 0 x(-49 + 16x2) = 0 (-49 * x + 16x2 * x) = 0 (-49x + 16x3) = 0 Solving -49x + 16x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-49 + 16x2) = 0 Factor a difference between two squares. x((7 + 4x)(-7 + 4x)) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(7 + 4x)' equal to zero and attempt to solve: Simplifying 7 + 4x = 0 Solving 7 + 4x = 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 + 4x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 4x = 0 + -7 4x = 0 + -7 Combine like terms: 0 + -7 = -7 4x = -7 Divide each side by '4'. x = -1.75 Simplifying x = -1.75Subproblem 3
Set the factor '(-7 + 4x)' equal to zero and attempt to solve: Simplifying -7 + 4x = 0 Solving -7 + 4x = 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 + 4x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 4x = 0 + 7 4x = 0 + 7 Combine like terms: 0 + 7 = 7 4x = 7 Divide each side by '4'. x = 1.75 Simplifying x = 1.75Solution
x = {0, -1.75, 1.75}
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