(7x-12)(4x+1)=0

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Solution for (7x-12)(4x+1)=0 equation:


Simplifying
(7x + -12)(4x + 1) = 0

Reorder the terms:
(-12 + 7x)(4x + 1) = 0

Reorder the terms:
(-12 + 7x)(1 + 4x) = 0

Multiply (-12 + 7x) * (1 + 4x)
(-12(1 + 4x) + 7x * (1 + 4x)) = 0
((1 * -12 + 4x * -12) + 7x * (1 + 4x)) = 0
((-12 + -48x) + 7x * (1 + 4x)) = 0
(-12 + -48x + (1 * 7x + 4x * 7x)) = 0
(-12 + -48x + (7x + 28x2)) = 0

Combine like terms: -48x + 7x = -41x
(-12 + -41x + 28x2) = 0

Solving
-12 + -41x + 28x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1 + -4x)(12 + -7x) = 0

Subproblem 1

Set the factor '(-1 + -4x)' equal to zero and attempt to solve: Simplifying -1 + -4x = 0 Solving -1 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -4x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4x = 0 + 1 -4x = 0 + 1 Combine like terms: 0 + 1 = 1 -4x = 1 Divide each side by '-4'. x = -0.25 Simplifying x = -0.25

Subproblem 2

Set the factor '(12 + -7x)' equal to zero and attempt to solve: Simplifying 12 + -7x = 0 Solving 12 + -7x = 0 Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -7x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -7x = 0 + -12 -7x = 0 + -12 Combine like terms: 0 + -12 = -12 -7x = -12 Divide each side by '-7'. x = 1.714285714 Simplifying x = 1.714285714

Solution

x = {-0.25, 1.714285714}

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