(4x+9)(14x-7)=0

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Solution for (4x+9)(14x-7)=0 equation:


Simplifying
(4x + 9)(14x + -7) = 0

Reorder the terms:
(9 + 4x)(14x + -7) = 0

Reorder the terms:
(9 + 4x)(-7 + 14x) = 0

Multiply (9 + 4x) * (-7 + 14x)
(9(-7 + 14x) + 4x * (-7 + 14x)) = 0
((-7 * 9 + 14x * 9) + 4x * (-7 + 14x)) = 0
((-63 + 126x) + 4x * (-7 + 14x)) = 0
(-63 + 126x + (-7 * 4x + 14x * 4x)) = 0
(-63 + 126x + (-28x + 56x2)) = 0

Combine like terms: 126x + -28x = 98x
(-63 + 98x + 56x2) = 0

Solving
-63 + 98x + 56x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-9 + 14x + 8x2) = 0

Factor a trinomial.
7((-9 + -4x)(1 + -2x)) = 0

Ignore the factor 7.

Subproblem 1

Set the factor '(-9 + -4x)' equal to zero and attempt to solve: Simplifying -9 + -4x = 0 Solving -9 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -4x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -4x = 0 + 9 -4x = 0 + 9 Combine like terms: 0 + 9 = 9 -4x = 9 Divide each side by '-4'. x = -2.25 Simplifying x = -2.25

Subproblem 2

Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5

Solution

x = {-2.25, 0.5}

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