(x-4)(4x+7)=0

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Solution for (x-4)(4x+7)=0 equation:


Simplifying
(x + -4)(4x + 7) = 0

Reorder the terms:
(-4 + x)(4x + 7) = 0

Reorder the terms:
(-4 + x)(7 + 4x) = 0

Multiply (-4 + x) * (7 + 4x)
(-4(7 + 4x) + x(7 + 4x)) = 0
((7 * -4 + 4x * -4) + x(7 + 4x)) = 0
((-28 + -16x) + x(7 + 4x)) = 0
(-28 + -16x + (7 * x + 4x * x)) = 0
(-28 + -16x + (7x + 4x2)) = 0

Combine like terms: -16x + 7x = -9x
(-28 + -9x + 4x2) = 0

Solving
-28 + -9x + 4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-7 + -4x)(4 + -1x) = 0

Subproblem 1

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 = -1.75

Subproblem 2

Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 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 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4

Solution

x = {-1.75, 4}

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