2(6x-7)(4x+3)=0

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Solution for 2(6x-7)(4x+3)=0 equation:


Simplifying
2(6x + -7)(4x + 3) = 0

Reorder the terms:
2(-7 + 6x)(4x + 3) = 0

Reorder the terms:
2(-7 + 6x)(3 + 4x) = 0

Multiply (-7 + 6x) * (3 + 4x)
2(-7(3 + 4x) + 6x * (3 + 4x)) = 0
2((3 * -7 + 4x * -7) + 6x * (3 + 4x)) = 0
2((-21 + -28x) + 6x * (3 + 4x)) = 0
2(-21 + -28x + (3 * 6x + 4x * 6x)) = 0
2(-21 + -28x + (18x + 24x2)) = 0

Combine like terms: -28x + 18x = -10x
2(-21 + -10x + 24x2) = 0
(-21 * 2 + -10x * 2 + 24x2 * 2) = 0
(-42 + -20x + 48x2) = 0

Solving
-42 + -20x + 48x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + -10x + 24x2) = 0

Factor a trinomial.
2((-3 + -4x)(7 + -6x)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-3 + -4x)' equal to zero and attempt to solve: Simplifying -3 + -4x = 0 Solving -3 + -4x = 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 + -4x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4x = 0 + 3 -4x = 0 + 3 Combine like terms: 0 + 3 = 3 -4x = 3 Divide each side by '-4'. x = -0.75 Simplifying x = -0.75

Subproblem 2

Set the factor '(7 + -6x)' equal to zero and attempt to solve: Simplifying 7 + -6x = 0 Solving 7 + -6x = 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 + -6x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -6x = 0 + -7 -6x = 0 + -7 Combine like terms: 0 + -7 = -7 -6x = -7 Divide each side by '-6'. x = 1.166666667 Simplifying x = 1.166666667

Solution

x = {-0.75, 1.166666667}

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