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

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


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

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

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

Multiply (-4 + 3x) * (7 + 2x)
4(-4(7 + 2x) + 3x * (7 + 2x)) = 0
4((7 * -4 + 2x * -4) + 3x * (7 + 2x)) = 0
4((-28 + -8x) + 3x * (7 + 2x)) = 0
4(-28 + -8x + (7 * 3x + 2x * 3x)) = 0
4(-28 + -8x + (21x + 6x2)) = 0

Combine like terms: -8x + 21x = 13x
4(-28 + 13x + 6x2) = 0
(-28 * 4 + 13x * 4 + 6x2 * 4) = 0
(-112 + 52x + 24x2) = 0

Solving
-112 + 52x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-28 + 13x + 6x2) = 0

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

Ignore the factor 4.

Subproblem 1

Set the factor '(-7 + -2x)' equal to zero and attempt to solve: Simplifying -7 + -2x = 0 Solving -7 + -2x = 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 + -2x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2x = 0 + 7 -2x = 0 + 7 Combine like terms: 0 + 7 = 7 -2x = 7 Divide each side by '-2'. x = -3.5 Simplifying x = -3.5

Subproblem 2

Set the factor '(4 + -3x)' equal to zero and attempt to solve: Simplifying 4 + -3x = 0 Solving 4 + -3x = 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 + -3x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3x = 0 + -4 -3x = 0 + -4 Combine like terms: 0 + -4 = -4 -3x = -4 Divide each side by '-3'. x = 1.333333333 Simplifying x = 1.333333333

Solution

x = {-3.5, 1.333333333}

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