(5x-3)(5x-3)=49x^2

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Solution for (5x-3)(5x-3)=49x^2 equation: 


Simplifying
(5x + -3)(5x + -3) = 49x2

Reorder the terms:
(-3 + 5x)(5x + -3) = 49x2

Reorder the terms:
(-3 + 5x)(-3 + 5x) = 49x2

Multiply (-3 + 5x) * (-3 + 5x)
(-3(-3 + 5x) + 5x * (-3 + 5x)) = 49x2
((-3 * -3 + 5x * -3) + 5x * (-3 + 5x)) = 49x2
((9 + -15x) + 5x * (-3 + 5x)) = 49x2
(9 + -15x + (-3 * 5x + 5x * 5x)) = 49x2
(9 + -15x + (-15x + 25x2)) = 49x2

Combine like terms: -15x + -15x = -30x
(9 + -30x + 25x2) = 49x2

Solving
9 + -30x + 25x2 = 49x2

Solving for variable 'x'.

Combine like terms: 25x2 + -49x2 = -24x2
9 + -30x + -24x2 = 49x2 + -49x2

Combine like terms: 49x2 + -49x2 = 0
9 + -30x + -24x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(3 + -10x + -8x2) = 0

Factor a trinomial.
3((1 + -4x)(3 + 2x)) = 0

Ignore the factor 3.

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 '(3 + 2x)' equal to zero and attempt to solve:

Simplifying
3 + 2x = 0

Solving
3 + 2x = 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 + 2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x = 0 + -3
2x = 0 + -3

Combine like terms: 0 + -3 = -3
2x = -3

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5
Solution
x = {0.25, -1.5}

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