(x+6)(4x-7)=0

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Solution for (x+6)(4x-7)=0 equation:


Simplifying
(x + 6)(4x + -7) = 0

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

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

Multiply (6 + x) * (-7 + 4x)
(6(-7 + 4x) + x(-7 + 4x)) = 0
((-7 * 6 + 4x * 6) + x(-7 + 4x)) = 0
((-42 + 24x) + x(-7 + 4x)) = 0
(-42 + 24x + (-7 * x + 4x * x)) = 0
(-42 + 24x + (-7x + 4x2)) = 0

Combine like terms: 24x + -7x = 17x
(-42 + 17x + 4x2) = 0

Solving
-42 + 17x + 4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-6 + -1x)(7 + -4x) = 0

Subproblem 1

Set the factor '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Divide each side by '-1'. x = -6 Simplifying x = -6

Subproblem 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 = 1.75

Solution

x = {-6, 1.75}

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